संख्यात्मक एकीकरण के लिए यहां 100 और अभ्यास प्रश्न दिए गए हैं:

       Integration 100 practice questions

401. Use the midpoint rule with 6 subintervals to approximate the value of ∫(2x + 3) dx from x = 1 to x = 5.

402. Estimate the definite integral ∫(x^2 + 4x) dx from x = -2 to x = 2 using the trapezoidal rule with 8 subintervals.

403. Approximate the value of ∫(e^x + sin(x)) dx from x = 0 to x = π using Simpson's rule with 10 subintervals.

404. Use Simpson's rule with 4 subintervals to compute the definite integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

405. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

406. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

407. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

408. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

409. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

410. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

411. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

412. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

413. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

414. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

415. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

416. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

417. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

418. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

419. Approximate the value of ∫(ln(x) + x^2

) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

420. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

421. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

422. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

423. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

424. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

425. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

426. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

427. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

428. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

429. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

430. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

431. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

432. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

433. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

434. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

435. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

436. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

437. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

438. Compute

 the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

439. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

440. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

441. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

442. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

443. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

444. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

445. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

446. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

447. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

448. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

449. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

450. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

451. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

452. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

453. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

454. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

455. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

456. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

457. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

458. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

459. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

460. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

461. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

462. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

463. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

464. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

465. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

466. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

467. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

468. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

469. Estimate the value of ∫(cos(x)

 - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

470. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

471. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

472. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

473. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

474. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

475. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

476. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

477. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

478. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

479. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

480. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

481. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

482. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

483. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

484. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

485. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

486. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

487. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

488. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

489. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

490. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

491. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

492. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.

493. Estimate the value of ∫(cos(x) - 2x) dx from x = 0 to x = π/2 using the midpoint rule with 12 subintervals.

494. Compute the definite integral ∫(3 + 2x) dx from x = 1 to x = 5 using the trapezoidal rule with 6 subintervals.

495. Approximate the value of ∫(ln(x) + 2x^2) dx from x = 1 to x = 4 using Simpson's rule with 8 subintervals.

496. Use Simpson's rule with 6 subintervals to estimate the integral ∫(4x^3 - 5x^2 + x) dx from x = -1 to x = 1.

497. Estimate the value of ∫(2x^3 - sin(x)) dx from x = 0 to x = 4 using the midpoint rule with 10 subintervals.

498. Compute the definite integral ∫(5 + 3x) dx from x = 2 to x = 6 using the trapezoidal rule with 5 subintervals.

499. Approximate the value of ∫(ln(x) + x^2) dx from x = 1 to x = 4 using Simpson's rule with 12 subintervals.

500. Use Simpson's rule with 4 subintervals to estimate the integral ∫(3x^3 - 2x^2 + x) dx from x = 1 to x = 3.