Advertisements
Advertisements
प्रश्न
Evaluate each of the following integral:
उत्तर
\[\int_0^\frac{\pi}{4} \tan xdx\]
\[ = \left.{\log\sec\ x}\right|_0^\frac{\pi}{4} \]
\[ = \log\sec\frac{\pi}{4} - \log\sec0\]
\[ = \log\sqrt{2} - \log1\]
\[ = \log 2^\frac{1}{2} - 0\]
\[ = \frac{1}{2}\log2\]
APPEARS IN
संबंधित प्रश्न
\[\int\limits_0^{( \pi )^{2/3}} \sqrt{x} \cos^2 x^{3/2} dx\]
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that \[\int_a^b xf\left( x \right)dx = \frac{a + b}{2} \int_a^b f\left( x \right)dx\]
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
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
Evaluate : \[\int\limits_0^{2\pi} \cos^5 x dx\] .
Evaluate : \[\int e^{2x} \cdot \sin \left( 3x + 1 \right) dx\] .
Evaluate : \[\int\frac{dx}{\sin^2 x \cos^2 x}\] .
\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]
Using second fundamental theorem, evaluate the following:
`int_1^"e" ("d"x)/(x(1 + logx)^3`
Evaluate the following:
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}` Find 'c" if `int_0^1 "f"(x) "d"x` = 2
Evaluate the following:
`int_0^oo "e"^(- x/2) x^5 "d"x`
Evaluate the following:
`int ((x^2 + 2))/(x + 1) "d"x`
`int "e"^x ((1 - x)/(1 + x^2))^2 "d"x` is equal to ______.
