Class 12 Math: Definite Integral

Class 12 Math

ID: 242 Type: Mcq Source: AISSCE(Board Exam) Year: 2025
Question 1: If \(f(2a-x)=f(x)\), then \(\int_{0}^{2a}f(x)dx\) is
  • A. \(\int_{0}^{2a}f(\frac{x}{2})dx\)
  • B. \(\int_{0}^{a}f(x)dx\)
  • C. \(2\int_{a}^{0}f(x)dx\)
  • D. \(2\int_{0}^{a}f(x)dx\)
ID: 304 Type: Mcq Source: AISSCE(Board Exam) Year: 2025
Question 2: The value of \(\int_{0}^{1}\frac{dx}{e^{x}+e^{-x}}\) is:
  • A. \(-\frac{\pi}{4}\)
  • B. \(\frac{\pi}{4}\)
  • C. \(\tan^{-1}e-\frac{\pi}{4}\)
  • D. \(\tan^{-1}e\)
ID: 319 Type: Mcq Source: AISSCE(Board Exam) Year: 2025
Question 3: \(\int_{0}^{\pi/2}\cos x\cdot e^{\sin x}dx\) is equal to:
  • A. 0
  • B. \(1-e\)
  • C. \(e-1\)
  • D. e
ID: 475 Type: Mcq Source: AISSCE(Board Exam) Year: 2024
Question 4: \(\int_{a}^{b}f(x)dx\) is equal to:
  • A. \(\int_{a}^{b}f(a-x)dx\)
  • B. \(\int_{a}^{b}f(a+b-x)dx\)
  • C. \(\int_{a}^{b}f(x-(a+b))dx\)
  • D. \(\int_{a}^{b}f((a-x)+(b-x))dx\)
ID: 493 Type: Mcq Source: AISSCE(Board Exam) Year: 2024
Question 5: \(\int_{0}^{\pi/2}\frac{\sin~x-\cos~x}{1+\sin~x~\cos~x}dx\) is equal to:
  • A. \(\pi\)
  • B. Zero (0)
  • C. \(\int_{0}^{\pi/2}\frac{2~\sin~x}{1+\sin~x~\cos~x}dx\)
  • D. \(\frac{\pi^{2}}{4}\)
ID: 511 Type: Mcq Source: AISSCE(Board Exam) Year: 2024
Question 6: \(\int_{-a}^{a}f(x)dx=0,\) if :
  • A. \(f(-x)=f(x)\)
  • B. \(f(-x)=-f(x)\)
  • C. \(f(a-x)=f(x)\)
  • D. \(f(a-x)=-f(x)\)
ID: 531 Type: Mcq Source: AISSCE(Board Exam) Year: 2024
Question 7: The value of \(\int_{0}^{3}\frac{dx}{\sqrt{9-x^{2}}}\) is:
  • A. \(\frac{\pi}{6}\)
  • B. \(\frac{\pi}{4}\)
  • C. \(\frac{\pi}{2}\)
  • D. \(\frac{\pi}{18}\)
ID: 553 Type: Mcq Source: AISSCE(Board Exam) Year: 2024
Question 8: The value of \(\int_{-1}^{1}x|x|dx\) is:
  • A. \(\frac{1}{6}\)
  • B. \(\frac{1}{3}\)
  • C. \(-\frac{1}{6}\)
  • D. 0
ID: 261 Type: Very short (VSA) Source: AISSCE(Board Exam) Year: 2025
Question 9: Evaluate: \(\int_{0}^{\frac{\pi}{4}}\sqrt{1+\sin 2x}dx\)
ID: 561 Type: Very short (VSA) Source: AISSCE(Board Exam) Year: 2024
Question 10: Evaluate: \(\int_{0}^{\pi/2}\sin~2x~\cos~3x~dx\)
ID: 572 Type: Very short (VSA) Source: AISSCE(Board Exam) Year: 2024
Question 11: Evaluate: \(\int_{0}^{\frac{\pi^{2}}{4}}\frac{\sin\sqrt{x}}{\sqrt{x}}dx\).
ID: 374 Type: Short (SA) Source: AISSCE(Board Exam) Year: 2025
Question 12: Evaluate: \(\int_{\pi/2}^{\pi}e^{x}(\frac{1-\sin x}{1-\cos x})dx\)
ID: 412 Type: Short (SA) Source: AISSCE(Board Exam) Year: 2025
Question 13: Evaluate: \(\int_{1}^{4}(|x-2|+|x-4|)dx\)
ID: 597 Type: Short (SA) Source: AISSCE(Board Exam) Year: 2024
Question 14: Evaluate : \(\int_{0}^{\pi}\frac{e^{cos~x}}{e^{cos~x}+e^{-cos~x}}d~x\)
ID: 598 Type: Short (SA) Source: AISSCE(Board Exam) Year: 2024
Question 15: Evaluate : \(\int_{-2}^{2}\sqrt{\frac{2-x}{2+x}}dx\)
ID: 599 Type: Short (SA) Source: AISSCE(Board Exam) Year: 2024
Question 16: Evaluate \(\int_{0}^{\frac{\pi}{4}}\frac{x~dx}{1+cos~2x+sin~2x}\)
ID: 612 Type: Short (SA) Source: AISSCE(Board Exam) Year: 2024
Question 17: Evaluate: \(\int_{0}^{\pi/4}\frac{1}{sin~x+cos~x}dx\)
ID: 613 Type: Short (SA) Source: AISSCE(Board Exam) Year: 2024
Question 18: Evaluate: \(\int_{1}^{3}(|x-1|+|x-2|+|x-3|)dx\).
ID: 383 Type: Long (LA) Source: AISSCE(Board Exam) Year: 2025
Question 19: Evaluate: \(\int_{0}^{\pi}\frac{dx}{a^{2}\cos^{2}x+b^{2}\sin^{2}x}\)
ID: 442 Type: Long (LA) Source: AISSCE(Board Exam) Year: 2025
Question 20: Evaluate: \(\int_{0}^{\pi/2}\frac{x}{\sin x+\cos x}dx\)
ID: 640 Type: Long (LA) Source: AISSCE(Board Exam) Year: 2024
Question 21: Evaluate: \(\int_{0}^{\frac{\pi}{4}}\frac{\sin x+\cos x}{9+16\sin 2x}dx\).
ID: 653 Type: Long (LA) Source: AISSCE(Board Exam) Year: 2024
Question 22: Evaluate: \(\int_{0}^{\frac{\pi}{2}}\sin 2x\tan^{-1}(\sin x)dx\).