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प्रश्न
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उत्तर
\[\int_0^3 \frac{1}{x^2 + 9} d x\]
\[ = \int_0^3 \frac{1}{x^2 + 3^2} d x\]
\[ = \frac{1}{3} \left[ \tan^{- 1} \frac{x}{3} \right]_0^3 \]
\[ = \frac{1}{3}\left( \tan^{- 1} 1 - \tan^{- 1} 0 \right)\]
\[ = \frac{1}{3}\left( \frac{\pi}{4} - 0 \right)\]
\[ = \frac{\pi}{12}\]
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संबंधित प्रश्न
Evaluate each of the following integral:
\[\int_a^b \frac{x^\frac{1}{n}}{x^\frac{1}{n} + \left( a + b - x \right)^\frac{1}{n}}dx, n \in N, n \geq 2\]
Evaluate each of the following integral:
Evaluate each of the following integral:
If \[\int\limits_0^1 \left( 3 x^2 + 2x + k \right) dx = 0,\] find the value of k.
\[\int\limits_0^4 x\sqrt{4 - x} dx\]
\[\int\limits_0^1 \tan^{- 1} x dx\]
\[\int\limits_0^1 \frac{1 - x}{1 + x} dx\]
\[\int\limits_0^{\pi/4} e^x \sin x dx\]
\[\int\limits_1^3 \left| x^2 - 4 \right| dx\]
\[\int\limits_{- 1/2}^{1/2} \cos x \log\left( \frac{1 + x}{1 - x} \right) dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \cot^7 x} dx\]
\[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} dx\]
\[\int\limits_0^\pi \cos 2x \log \sin x dx\]
Find : `∫_a^b logx/x` dx
Evaluate the following using properties of definite integral:
`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x) "d"x`
Evaluate the following:
`int_0^oo "e"^(-4x) x^4 "d"x`
Evaluate the following integrals as the limit of the sum:
`int_1^3 (2x + 3) "d"x`
Evaluate the following integrals as the limit of the sum:
`int_0^1 x^2 "d"x`
