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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-08-ABC-01
Area Between Two Curves — Assignment
Chapter: Application of Integrals
Topic: Area Between Two Curves
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.
Area between $y=x$ and $y=x^2$ on $[0,1]$ is:
  • A.$\tfrac16$
  • B.$\tfrac13$
  • C.$\tfrac12$
  • D.$1$
2.
The limits for area between two curves come from:
  • A.the $y$-intercepts
  • B.their intersection points
  • C.the origin
  • D.the derivative
3.
Area between $y=x^2$ and $y=4$ is:
  • A.$\tfrac{32}{3}$
  • B.$8$
  • C.$16$
  • D.$\tfrac{16}{3}$
4.
The integrand for area between curves should be:
  • A.always $f+g$
  • B.upper minus lower
  • C.lower minus upper
  • D.$f\cdot g$
5.
Area between curves $=$
  • A.$\int_a^b(f-g)\,dx$
  • B.$\int_a^b fg\,dx$
  • C.$\int_a^b f\,dx$
  • D.$f(b)-g(a)$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the area between $y=x$ and $y=x^2$ from their intersections.
7.
Find the intersection points of $y=2x$ and $y=x^2$.
8.
On $(0,1)$, which is upper: $\sqrt{x}$ or $x$?
9.
Find the area between $y=2x$ and $y=x^2$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area between $y=x^2$ and $y=4$.
11.
Find the area between $y=\sqrt{x}$ and $y=x$ for $0\le x\le 1$.
12.
Find the area between $y=x^2$ and $y=2x$.
13.
Find the area between the line $y=x$ and the curve $y=x^3$ in the first quadrant.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the area of the region bounded by the parabola $y^2=4x$ and the line $y=2x$.
15.
Find the area enclosed between the parabola $y=x^2$ and the line $y=x+2$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\tfrac16$
  2. (B) their intersection points
  3. (A) $\tfrac{32}{3}$
  4. (B) upper minus lower
  5. (A) $\int_a^b(f-g)\,dx$
Section B — Short Answer (2 marks)
  1. $\tfrac16$ sq unit.
  2. $(0,0)$ and $(2,4)$.
  3. $\sqrt{x}$.
  4. $\tfrac43$ sq units.
Section C — Short Answer (3 marks)
  1. $\tfrac{32}{3}$ sq units.
  2. $\tfrac16$ sq unit.
  3. $\tfrac43$ sq units.
  4. $\tfrac14$ sq unit.
Section D — Long Answer (5 marks)
  1. $\tfrac13$ sq unit.
  2. $\tfrac92$ sq units.
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