JEE (Main) Mathematics - INTEGRAL CALCULAS Multiple Choice Questions (MCQs)

JEE (Main) Mathematics - Integral Calculus Multiple Choice Questions (MCQs)

1. What is the integral of \( x^n \) (where \( n \neq -1 \))?
   a) \( \frac{x^{n+1}}{n+1} + C \)
   b) \( \frac{x^{n-1}}{n-1} + C \)
   c) \( x^{n+1} + C \)
   d) \( \frac{n}{x^{n+1}} + C \)
   Answer: a) \( \frac{x^{n+1}}{n+1} + C \)
2. What is the integral of \( \cos(x) \)?
   a) \( \sin(x) + C \)
   b) \( -\cos(x) + C \)
   c) \( \tan(x) + C \)
   d) \( -\sin(x) + C \)
   Answer: a) \( \sin(x) + C \)
3. What is the integral of \( e^x \)?
   a) \( e^x + C \)
   b) \( \ln(x) + C \)
   c) \( e^{-x} + C \)
   d) \( x e^x + C \)
   Answer: a) \( e^x + C \)
4. What is the integral of \( \sin(x) \)?
   a) \( -\cos(x) + C \)
   b) \( \cos(x) + C \)
   c) \( -\sin(x) + C \)
   d) \( \tan(x) + C \)
   Answer: a) \( -\cos(x) + C \)
5. The integral of \( \frac{1}{x} \) is:
   a) \( \ln(x) + C \)
   b) \( e^x + C \)
   c) \( x \ln(x) + C \)
   d) \( x^2 + C \)
   Answer: a) \( \ln(x) + C \)
6. What is the integral of \( \sec^2(x) \)?
   a) \( \tan(x) + C \)
   b) \( \sec(x) + C \)
   c) \( \sin(x) + C \)
   d) \( \cos(x) + C \)
   Answer: a) \( \tan(x) + C \)
7. What is the integral of \( \frac{1}{1+x^2} \)?
   a) \( \tan^{-1}(x) + C \)
   b) \( \ln(1+x^2) + C \)
   c) \( \sin^{-1}(x) + C \)
   d) \( e^x + C \)
   Answer: a) \( \tan^{-1}(x) + C \)
8. What is the integral of \( \ln(x) \)?
   a) \( x \ln(x) - x + C \)
   b) \( \frac{x}{\ln(x)} + C \)
   c) \( x \ln(x) + C \)
   d) \( e^x \ln(x) + C \)
   Answer: a) \( x \ln(x) - x + C \)
9. The integral of \( \sec(x) \tan(x) \) is:
   a) \( \sec(x) + C \)
   b) \( \tan(x) + C \)
   c) \( \ln(\sec(x)) + C \)
   d) \( -\cos(x) + C \)
   Answer: a) \( \sec(x) + C \)
10. What is the integral of \( e^{ax} \)?
    a) \( \frac{e^{ax}}{a} + C \)
    b) \( e^{ax} + C \)
    c) \( \frac{e^{ax}}{a^2} + C \)
    d) \( ax e^{ax} + C \)
    Answer: a) \( \frac{e^{ax}}{a} + C \)
11. The integral of \( \cos(ax) \) is:
    a) \( \frac{\sin(ax)}{a} + C \)
    b) \( \frac{\cos(ax)}{a} + C \)
    c) \( \sin(ax) + C \)
    d) \( a \sin(ax) + C \)
    Answer: a) \( \frac{\sin(ax)}{a} + C \)
12. What is the integral of \( \tan(x) \)?
    a) \( \ln(\sec(x)) + C \)
    b) \( \ln(\tan(x)) + C \)
    c) \( \sin(x) + C \)
    d) \( \sec(x) + C \)
    Answer: a) \( \ln(\sec(x)) + C \)
13. The integral of \( \frac{1}{\sqrt{1 - x^2}} \) is:
    a) \( \sin^{-1}(x) + C \)
    b) \( \ln(1 - x^2) + C \)
    c) \( \cos^{-1}(x) + C \)
    d) \( e^{x} + C \)
    Answer: a) \( \sin^{-1}(x) + C \)
14. What is the integral of \( \frac{1}{x^2} \)?
    a) \( -\frac{1}{x} + C \)
    b) \( \frac{1}{x} + C \)
    c) \( -\frac{1}{x^2} + C \)
    d) \( \ln(x) + C \)
    Answer: a) \( -\frac{1}{x} + C \)
15. What is the integral of \( \sqrt{1 - x^2} \)?
    a) \( \frac{x \sqrt{1 - x^2}}{2} + \frac{1}{2} \sin^{-1}(x) + C \)
    b) \( \ln(1 - x^2) + C \)
    c) \( \frac{1}{3} x^3 + C \)
    d) \( \sin^{-1}(x) + C \)
    Answer: a) \( \frac{x \sqrt{1 - x^2}}{2} + \frac{1}{2} \sin^{-1}(x) + C \)

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