MCQs of Integrals

Showing 221 to 230 out of 421 Questions

221.

\int_{0}^{\frac{π}{2}} \frac{(\sin x)^{2006}}{(\sin x)^{2006} + (\cos x)^{2006}} d x

= _____

222.

\int_{0}^{4014} \frac{2^{x}}{2^{x} + 2^{4014 - x}} d x

= _____

223.

\int_{0}^{\frac{π}{2}} \frac{2008^{\sin x}}{2008^{\sin x} + 2008^{\cos x}} d x

= _____

224.

\int_{π}^{\frac{3 π}{2}} (\frac{5 π}{2} x - x^{2}) \cos 2 x d x

= _____

225.

If f(x) is odd function then

\int_{- \frac{π}{2}}^{\frac{π}{2}} f (\cos x) d x

= _____

226.

If f : R → R and g : R → R are continuous functions then

\int_{- \frac{π}{2}}^{\frac{π}{2}} {f (x) + f (- x)} {g (x) - g (- x)} d x

= _____

227.

\int_{- 1}^{1} \sin^{11} x d x

= _____

(a)	0
(b)	1
(c)	$\frac{10}{11} x \frac{8}{9} x \frac{6}{7} x \frac{4}{6} x \frac{2}{3}$
(d)	$\frac{10}{11} x \frac{8}{9} x \frac{6}{7} x \frac{4}{5} x \frac{2}{3} x \frac{π}{2}$

228.

\int_{- 1}^{1} \frac{e^{x} + 1}{e^{x} - 1} d x

= _____

229.

f (x) = \int_{1}^{x} \sqrt{2 - t^{2}} dt

, then solution of x² - f'(x) = 0 is _____

230.

\int_{0}^{1000} e^{x - [x]} d x

= _____

Showing 221 to 230 out of 421 Questions