Question types

Application of Definite Integration question types

164 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

164
Questions
7
Question groups
5
Question types
Sample Questions

Application of Definite Integration questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The area of the region included between the line $x+y=1$ and the circle $x^2+y^2=1$ is
  • A
    $\frac{\pi}{2}-1$ sq units
  • B
    π – 2 sq units
  • $\frac{\pi}{4}-\frac{1}{2}$ sq units
  • D
    $\pi-\frac{1}{2}$ sq units

Answer: C.

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Q 2MCQ1 Mark
The area of the region included between the parabolas $y^2=4 a x$ and $x^2=4 a y,(a>0)$ is

given by

  • $\frac{16 a^2}{3}$ sq units
  • B
    $\frac{8 a^2}{3}$ sq units
  • C
    $\frac{4 a^2}{3}$ sq units
  • D
    $\frac{32 a^2}{3}$ sq units

Answer: A.

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Q 3MCQ1 Mark
The area of the region bounded by $x^2=16 y, y=1, y=4$ and $x=0$ in the first quadrant, is
  • A
    $\frac{7}{3}$ sq units
  • B
    $\frac{8}{3}$ sq units
  • C
    $\frac{64}{3}$ sq units
  • $\frac{56}{3}$ sq units

Answer: D.

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Q 4MCQ1 Mark
The area bounded by the curve $y=\tan x$, X-axis and the line $x=\frac{\pi}{4}$ is
  • $\frac{1}{3} \log 2 sq$ units
  • B
    log 2 sq units
  • C
    2 log 2 sq units
  • D
    3 log 2 sq units

Answer: A.

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Q 5MCQ1 Mark
The area enclosed between the two parabolas $y^2=4 x$ and $y=x$ is
  • A
    $\frac{8}{3}$ sq units
  • B
    $\frac{32}{3}$ sq units
  • $\frac{16}{3} sq$ units
  • D
    $\frac{4}{3}$ sq units

Answer: C.

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Find the area of the regions bounded by the following curve, the $\mathrm{X}$-axis and the given lines :
(i) $y=x^2, x=1, x=2$
(ii) $y^2=4 x, x=1, x=4, y \geq 0$
(iii) $y=\sin x, x=-\frac{\pi}{2}, x=\frac{\pi}{2}$
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