GATE · Engineering Mathematics

Integration

15 practice questions, each with the answer and an explanation.

Practise Integration now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 15 questions

  1. Evaluate .
  2. Evaluate .
  3. Evaluate .
  4. Evaluate .
  5. Evaluate .
  6. Evaluate .
  7. Evaluate .
  8. Evaluate .
  9. Evaluate .
  10. Evaluate the double integral I = ∫_(0 to 1) ∫_(y to 1) e^(x^2) dx dy by reversing the order of integration.
  11. Using Cauchy's residue theorem, evaluate the contour integral ∮_C [z^2 / (z - 2)] dz counterclockwise around the circle C: |z| = 3.
  12. What is the value of the line integral ∮_C (y dx - x dy) around the boundary of the ellipse x^2/a^2 + y^2/b^2 = 1 traversed counterclockwise?
  13. Evaluate the improper integral I = ∫_(0 to ∞) x^3 * e^(-2x) dx using the Gamma function.
  14. What is the value of ∮_C [e^z / (z^2 + 1)] dz taken counterclockwise along the circle |z - i| = 1?
  15. Evaluate the surface integral ∬_S F · n dS, where F = x i + y j + z k and S is the closed sphere x^2 + y^2 + z^2 = R^2 with outward unit normal n.

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