Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\int_0^1 \frac{1}{1 + x^2} d x\]
\[ = \left[ \tan^{- 1} x \right]_0^1 \]
\[ = \frac{\pi}{4} - 0\]
\[ = \frac{\pi}{4}\]
APPEARS IN
संबंधित प्रश्न
Evaluate each of the following integral:
Evaluate each of the following integral:
\[\int_a^b \frac{x^\frac{1}{n}}{x^\frac{1}{n} + \left( a + b - x \right)^\frac{1}{n}}dx, n \in N, n \geq 2\]
\[\int\limits_0^\pi \frac{1}{1 + \sin x} dx\] equals
The value of \[\int\limits_0^\pi \frac{x \tan x}{\sec x + \cos x} dx\] is __________ .
\[\int\limits_0^4 x\sqrt{4 - x} dx\]
\[\int\limits_1^2 \frac{x + 3}{x\left( x + 2 \right)} dx\]
\[\int\limits_{- a}^a \frac{x e^{x^2}}{1 + x^2} dx\]
\[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} dx\]
\[\int\limits_0^1 \cot^{- 1} \left( 1 - x + x^2 \right) dx\]
\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]
\[\int\limits_0^2 \left( 2 x^2 + 3 \right) dx\]
\[\int\limits_0^3 \left( x^2 + 1 \right) dx\]
Find : `∫_a^b logx/x` dx
Using second fundamental theorem, evaluate the following:
`int_0^(pi/2) sqrt(1 + cos x) "d"x`
Verify the following:
`int (x - 1)/(2x + 3) "d"x = x - log |(2x + 3)^2| + "C"`
`int x^9/(4x^2 + 1)^6 "d"x` is equal to ______.
`int x^3/(x + 1)` is equal to ______.
