اردو

Home / Practice / Class 12 / Mathematics / Integration

Integration

Written by Hassan Raza (Mathematics)

8 Class 12 Mathematics questions with answers and explanations.

Printable worksheet with answer key

All questions with answers
  1. The integral of x³ dx is:

    • 1 x⁴ / 4 + c
    • 2 3x² + c
    • 3 x³ / 3 + c
    • 4 x⁴ + c
    Show answer

    Correct answer: x⁴ / 4 + c

    Add one to the power and divide by it.

    Report a mistake

  2. The integral of cos x dx is:

    • 1 -cos x + c
    • 2 cos x + c
    • 3 -sin x + c
    • 4 sin x + c
    Show answer

    Correct answer: sin x + c

    d/dx(sin x) = cos x.

    Report a mistake

  3. The integral of 1/x dx is:

    • 1 ln|x| + c
    • 2 -1/x² + c
    • 3 x + c
    • 4 1/x² + c
    Show answer

    Correct answer: ln|x| + c

    d/dx(ln x) = 1/x.

    Report a mistake

  4. The definite integral of 2x dx from 0 to 3 is:

    • 1 6
    • 2 3
    • 3 9
    • 4 18
    Show answer

    Correct answer: 9

    [x²] from 0 to 3 = 9.

    Report a mistake

  5. The area under y = x from x = 0 to x = 4 is:

    • 1 16
    • 2 8
    • 3 4
    • 4 2
    Show answer

    Correct answer: 8

    The integral of x is x²/2, giving 16/2 = 8.

    Report a mistake

  6. The integral of e^x dx is:

    • 1 x e^x + c
    • 2 1/x + c
    • 3 e^x + c
    • 4 e^(x+1) + c
    Show answer

    Correct answer: e^x + c

    e^x is its own antiderivative.

    Report a mistake

  7. The integral of sin x dx is:

    • 1 -cos x + c
    • 2 sin x + c
    • 3 cos x + c
    • 4 -sin x + c
    Show answer

    Correct answer: -cos x + c

    d/dx(-cos x) = sin x.

    Report a mistake

  8. The definite integral of 3x² dx from 0 to 2 is:

    • 1 4
    • 2 8
    • 3 6
    • 4 12
    Show answer

    Correct answer: 8

    [x³] from 0 to 2 = 8.

    Report a mistake

More Mathematics topics