Question

$\int_{- 100\pi}^{100\pi}{(\sin^{4}x + \cos^{4}x)dx}$is equal to -

• A. 100 p
• B. 150 p
• C. 200 p
• D. None

Answer 1

Answer: (B)

150 p

Answer 2

$\int_{- 100\pi}^{100\pi}{(\sin^{4}x + \cos^{4}x)dx}$= 2$\int_{- 100\pi}^{100\pi}{(\sin^{4}x + \cos^{4}x)dx}$

(Q integrand is given)

= 2$\int_{0}^{\frac{\pi}{2}(200)}{(\sin^{4}x + \cos^{4}x)dx}$= 2 . 200

$\int_{0}^{\pi/2}{(\sin^{4}x + \cos^{4}x)}$dx

$\left\lbrack \because\sin^{4}x + \cos^{4}xisaperiodicfunctionofperiod\frac{\pi}{2} \right\rbrack$

= 400 $\left\lbrack \int_{0}^{\pi/2}{\sin^{4}x + \int_{0}^{\pi/2}{\cos^{4}\left( \frac{\pi}{2} - x \right)}dx} \right\rbrack$

= 800 $\int _ { 0 } ^ { \pi / 2 } \sin ^ { 4 } x$ dx = 800 . $\frac { 3.1 } { 4.2 }$ · $\frac { \pi } { 2 }$ = 150 p.

Hence (2) is the correct answer.