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 integral:
If `f` is an integrable function such that f(2a − x) = f(x), then prove that
Evaluate each of the following integral:
If \[\left[ \cdot \right] and \left\{ \cdot \right\}\] denote respectively the greatest integer and fractional part functions respectively, evaluate the following integrals:
\[\int\limits_0^\pi \frac{1}{1 + \sin x} dx\] equals
\[\int_0^\frac{\pi^2}{4} \frac{\sin\sqrt{x}}{\sqrt{x}} dx\] equals
The value of the integral \[\int\limits_{- 2}^2 \left| 1 - x^2 \right| dx\] is ________ .
Evaluate : \[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\] .
\[\int\limits_0^\infty \frac{x}{\left( 1 + x \right)\left( 1 + x^2 \right)} dx\]
\[\int\limits_1^2 \frac{1}{x^2} e^{- 1/x} dx\]
\[\int\limits_{\pi/3}^{\pi/2} \frac{\sqrt{1 + \cos x}}{\left( 1 - \cos x \right)^{5/2}} dx\]
Evaluate the following integrals :-
\[\int_2^4 \frac{x^2 + x}{\sqrt{2x + 1}}dx\]
\[\int\limits_0^1 \left| 2x - 1 \right| dx\]
\[\int\limits_{- a}^a \frac{x e^{x^2}}{1 + x^2} dx\]
\[\int\limits_0^{2\pi} \cos^7 x dx\]
\[\int\limits_0^\pi \frac{x \sin x}{1 + \cos^2 x} dx\]
Evaluate the following:
Γ(4)
Choose the correct alternative:
`Γ(3/2)`
`int x^9/(4x^2 + 1)^6 "d"x` is equal to ______.
What does a definite integral represent?
What is an antiderivative of \[x\]?
