ECAT Pakistan · Mathematics

Integration and Differential Equations

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

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

All 9 questions

  1. Evaluate the definite integral: integral from 0 to 1 of x * e^(2x) dx.
  2. What is the area of the region enclosed between the parabola y = x^2 and the line y = 2x?
  3. Solve the first-order differential equation dy/dx + (2/x) y = 4x with initial condition y(1) = 2.
  4. Evaluate: integral of dx / (x^2 + 4x + 13).
  5. What is the general solution of the separable differential equation dy/dx = (1 + y^2) / (1 + x^2)?
  6. Evaluate the definite integral: integral from 0 to pi/2 of sin^3(x) * cos(x) dx.
  7. What is the order and degree of the differential equation: [1 + (dy/dx)^2]^(3/2) = 5 * d^2y/dx^2?
  8. Evaluate: integral of (2x + 3) / (x^2 + 3x - 10) dx.
  9. What is the value of the definite integral of an odd continuous function f(x) over the symmetric interval [-a, a]?

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