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Integration

Class 12 · Mathematics · 8 questions

Name: ____________________   Date: ____________

  1. The integral of x³ dx is:

    • A x⁴ / 4 + c
    • B 3x² + c
    • C x³ / 3 + c
    • D x⁴ + c
  2. The integral of cos x dx is:

    • A -cos x + c
    • B cos x + c
    • C -sin x + c
    • D sin x + c
  3. The integral of 1/x dx is:

    • A ln|x| + c
    • B -1/x² + c
    • C x + c
    • D 1/x² + c
  4. The definite integral of 2x dx from 0 to 3 is:

    • A 6
    • B 3
    • C 9
    • D 18
  5. The area under y = x from x = 0 to x = 4 is:

    • A 16
    • B 8
    • C 4
    • D 2
  6. The integral of e^x dx is:

    • A x e^x + c
    • B 1/x + c
    • C e^x + c
    • D e^(x+1) + c
  7. The integral of sin x dx is:

    • A -cos x + c
    • B sin x + c
    • C cos x + c
    • D -sin x + c
  8. The definite integral of 3x² dx from 0 to 2 is:

    • A 4
    • B 8
    • C 6
    • D 12

Answer key

1. A, 2. D, 3. A, 4. C, 5. B, 6. C, 7. A, 8. B

  1. Add one to the power and divide by it.

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

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

  4. [x²] from 0 to 3 = 9.

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

  6. e^x is its own antiderivative.

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

  8. [x³] from 0 to 2 = 8.