← Back to topic
Vidaara.orgClass 12 · Mathematics
CodeVID-M12-08-AUC-01
Area Under a Curve — Assignment
Chapter: Application of Integrals
Topic: Area Under a Curve
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The area under $y=x^2$ from $0$ to $3$ is:
  • A.$9$
  • B.$27$
  • C.$3$
  • D.$6$
2.
$\displaystyle\int_0^{\pi}\sin x\,dx$ (area) equals:
  • A.$0$
  • B.$1$
  • C.$2$
  • D.$\pi$
3.
If $f(x)<0$ on part of $[a,b]$, area is found using:
  • A.the plain integral
  • B.absolute values of the pieces
  • C.the derivative
  • D.half the integral
4.
Area bounded by $x=y^2$ and $x=4$ (first quadrant) is:
  • A.$\tfrac{16}{3}$
  • B.$8$
  • C.$\tfrac{8}{3}$
  • D.$16$
5.
Area under a curve $y=f(x)$ above the $x$-axis is:
  • A.$\int f'\,dx$
  • B.$\int_a^b f(x)\,dx$
  • C.$f(b)-f(a)$
  • D.$\int x\,dy$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the area under $y=x^2$ from $x=0$ to $x=2$.
7.
Find the area under $y=2x$ from $x=0$ to $x=3$.
8.
Find the area under $y=x^3$ from $x=0$ to $x=1$.
9.
Find the area under $y=\cos x$ from $0$ to $\tfrac{\pi}{2}$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area bounded by $y=x^2$, the $x$-axis and $x=3$.
11.
Find the area under $y=\sin x$ from $0$ to $\pi$.
12.
Find the area of the region bounded by $x=y^2$ and $x=4$ in the first quadrant.
13.
Find the area under $y=x^2+1$ from $x=0$ to $x=2$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the area enclosed by the circle $x^2+y^2=4$.
15.
Find the area bounded by $y=x^2$ and the $x$-axis between $x=-2$ and $x=2$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $9$
  2. (C) $2$
  3. (B) absolute values of the pieces
  4. (A) $\tfrac{16}{3}$
  5. (B) $\int_a^b f(x)\,dx$
Section B — Short Answer (2 marks)
  1. $\tfrac{8}{3}$ sq units.
  2. $9$ sq units.
  3. $\tfrac14$ sq unit.
  4. $1$ sq unit.
Section C — Short Answer (3 marks)
  1. $9$ sq units.
  2. $2$ sq units.
  3. $\tfrac{16}{3}$ sq units.
  4. $\tfrac{14}{3}$ sq units.
Section D — Long Answer (5 marks)
  1. $4\pi$ sq units.
  2. $\tfrac{16}{3}$ sq units.
Generated by Vidaara.org · Assignment VID-M12-08-AUC-01 · vidaara.org