Advertisements
Advertisements
प्रश्न
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
Advertisements
उत्तर
\[\text{We have}, \]
\[ \int_0^a 3 x^2 d x = 8\]
\[ \Rightarrow \left[ 3\frac{x^3}{3} \right]_0^a = 8\]
\[ \Rightarrow \left[ x^3 \right]_0^a = 8\]
\[ \Rightarrow a^3 - 0 = 8\]
\[ \Rightarrow a = \sqrt[3]{8}\]
\[ = 2\]
APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals:
If \[\int_0^a \frac{1}{4 + x^2}dx = \frac{\pi}{8}\] , find the value of a.
`int_0^1 sqrt((1 - "x")/(1 + "x")) "dx"`
Given that \[\int\limits_0^\infty \frac{x^2}{\left( x^2 + a^2 \right)\left( x^2 + b^2 \right)\left( x^2 + c^2 \right)} dx = \frac{\pi}{2\left( a + b \right)\left( b + c \right)\left( c + a \right)},\] the value of \[\int\limits_0^\infty \frac{dx}{\left( x^2 + 4 \right)\left( x^2 + 9 \right)},\]
The value of \[\int\limits_0^\pi \frac{1}{5 + 3 \cos x} dx\] is
Evaluate : \[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\] .
\[\int\limits_0^{\pi/2} \frac{\cos x}{1 + \sin^2 x} dx\]
\[\int\limits_0^1 \log\left( 1 + x \right) dx\]
\[\int\limits_1^3 \left| x^2 - 2x \right| dx\]
\[\int\limits_{- a}^a \frac{x e^{x^2}}{1 + x^2} dx\]
\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]
\[\int\limits_0^\pi \frac{dx}{6 - \cos x}dx\]
\[\int\limits_1^4 \left( x^2 + x \right) dx\]
