Advertisements
Advertisements
प्रश्न
\[\int\limits_{\pi/3}^{\pi/2} \frac{\sqrt{1 + \cos x}}{\left( 1 - \cos x \right)^{5/2}} dx\]
Advertisements
उत्तर
\[\int_\frac{\pi}{3}^\frac{\pi}{2} \frac{\sqrt{1 + \cos x}}{\left( 1 - \cos x \right)^\frac{5}{2}} d x\]
\[ = \int_\frac{\pi}{3}^\frac{\pi}{2} \frac{\sqrt{1 + \cos x}}{\left( 1 - \cos x \right)^\frac{5}{2}} \times \frac{\sqrt{1 - \cos x}}{\sqrt{1 - \cos x}} d x\]
\[ = \int_\frac{\pi}{3}^\frac{\pi}{2} \frac{\sin x}{\left( 1 - \cos x \right)^3}dx\]
\[ = - \frac{1}{2} \left[ \left( 1 - \cos x \right)^{- 2} \right]_\frac{\pi}{3}^\frac{\pi}{2} \]
\[ = - \frac{1}{2}\left[ 1 - 4 \right]\]
\[ = \frac{3}{2}\]
APPEARS IN
संबंधित प्रश्न
\[\int\limits_{\pi/4}^{\pi/2} \cot x\ dx\]
If `f` is an integrable function such that f(2a − x) = f(x), then prove that
If \[\int_0^a \frac{1}{4 + x^2}dx = \frac{\pi}{8}\] , find the value of a.
The value of the integral \[\int\limits_0^{\pi/2} \frac{\sqrt{\cos x}}{\sqrt{\cos x} + \sqrt{\sin x}} dx\] is
If \[\int\limits_0^1 f\left( x \right) dx = 1, \int\limits_0^1 xf\left( x \right) dx = a, \int\limits_0^1 x^2 f\left( x \right) dx = a^2 , then \int\limits_0^1 \left( a - x \right)^2 f\left( x \right) dx\] equals
The value of the integral \[\int\limits_{- 2}^2 \left| 1 - x^2 \right| dx\] is ________ .
If f (a + b − x) = f (x), then \[\int\limits_a^b\] x f (x) dx is equal to
\[\int\limits_0^1 \tan^{- 1} x dx\]
\[\int\limits_0^{15} \left[ x^2 \right] dx\]
\[\int\limits_0^{\pi/2} \frac{dx}{4 \cos x + 2 \sin x}dx\]
Find : `∫_a^b logx/x` dx
Evaluate the following using properties of definite integral:
`int_0^1 log (1/x - 1) "d"x`
Evaluate the following using properties of definite integral:
`int_0^1 x/((1 - x)^(3/4)) "d"x`
If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4ex + 5e –x| + C, then ______.
`int (x + 3)/(x + 4)^2 "e"^x "d"x` = ______.
Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`
