# Application of Integrals

This is an MCQ-based quiz on the Application of Integrals.

This includes Area under Simple Curves and Area between Two Curves.

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The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ π / 2 is

√2 sq.units (√2 + 1) sq. units (√2 – 1) sq. units (2√2 – 1) sq.units

The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is

3/8 sq.units 5/8 sq.units 7/8 sq.units 9/8 sq. units

The area of the region bounded by the curve y = sqrt(16-x^2) and x-axis is

8π sq.units 20π sq. units 16π sq. units 256π sq. units

Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32 is

16π sq.units 4π sq. units 32π sq. units 24π sq. units

Area of the region bounded by the curve y = cos x between x = 0 and x = π is

2 sq. units 4 sq, units 3 sq.units 1 sq. units

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

2 (π – 2) π – 2 2π – 1 2 (π + 2).

Area lying between the curves y² = 4x and y = 2 is:

2/3 1/3 1/4 3/4

Area bounded by the curve y = x³, the x-axis and the ordinates x = -2 and x = 1 is

-9 –15/4 15/4 17/4

The area bounded by the curve y = x|x|, x-axis and the ordinates x = -1 and x = 1 is given by

0 –1/3 2/3 4/3

The area of the region bounded by the curve x = 2y + 3 and the lines y = 1 and y = -1 is

4 sq. units 3/2 sq. units 6 sq. units 8 sq, units

If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is

9/2 sq. units 8 sq. units 12 sq. units 4 sq. unjts

Area bounded by the lines y = |x| – 2 and y = 1 – |x – 1| is equal to

4 sq. units 6 sq. units 2 sq. units 8 sq. units

The area bounded by the lines y = |x| – 1 and y = -|x| + 1 is

1 sq. unit 2 sq. unit 2√2 sq. units 4 sq. units

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is

2

9/4

9/3

9/2

The area of the region bounded by the circle x² + y² = 1 is

2π sq. units

π sq. units

3π sq. units

4π sq. units

Quiz/Test Summary
Title: Application of Integrals
Questions: 15
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