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Question

Question: If A = \(\int _ { 0 } ^ { \pi / 2 } \sin ^ { 2 } x\) dx and B = <img src="https://cdn.pureessence.t...

If A = ∫0π/2sin⁡2x\int _ { 0 } ^ { \pi / 2 } \sin ^ { 2 } x dx and B = and C = then -

A

A + B = 0

B

A – B = 0

C

A + C = 0

D

A – C = 0

Answer

A – B = 0

Explanation

Solution

A – B = ∫0π/2(sin⁡2x−cos⁡2x)dx\int _ { 0 } ^ { \pi / 2 } \left( \sin ^ { 2 } x - \cos ^ { 2 } x \right) d x

= 12⋅π2−12⋅π2\frac { 1 } { 2 } \cdot \frac { \pi } { 2 } - \frac { 1 } { 2 } \cdot \frac { \pi } { 2 } [walli's formula]