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Question: Area bounded by the curves y = sin<img src="https://cdn.pureessence.tech/canvas_347.png?top_left_x=4...

Area bounded by the curves y = sinand y = x3, is equal to

A

4−ππ\frac { 4 - \pi } { \pi } sq. units

B

4−π2π\frac { 4 - \pi } { 2 \pi }sq. units

C

8−ππ\frac { 8 - \pi } { \pi } sq. units

D

8−π2π\frac { 8 - \pi } { 2 \pi }sq. units

Answer

8−π2π\frac { 8 - \pi } { 2 \pi }sq. units

Explanation

Solution

Bounded area,

Δ=2∫01(sin⁡πx2−x3)dx\Delta = 2 \int _ { 0 } ^ { 1 } \left( \sin \frac { \pi x } { 2 } - x ^ { 3 } \right) d x

=2(−2πcos⁡πx2−x44)01=2(2π−14)=8−π2π= 2 \left( - \frac { 2 } { \pi } \cos \frac { \pi x } { 2 } - \frac { x ^ { 4 } } { 4 } \right) _ { 0 } ^ { 1 } = 2 \left( \frac { 2 } { \pi } - \frac { 1 } { 4 } \right) = \frac { 8 - \pi } { 2 \pi }