Advertisements
Advertisements
Question
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
Advertisements
Solution
\[\text{We have}, \]
\[ \int_0^a 3 x^2 d x = 8\]
\[ \Rightarrow \left[ 3\frac{x^3}{3} \right]_0^a = 8\]
\[ \Rightarrow \left[ x^3 \right]_0^a = 8\]
\[ \Rightarrow a^3 - 0 = 8\]
\[ \Rightarrow a = \sqrt[3]{8}\]
\[ = 2\]
APPEARS IN
RELATED QUESTIONS
If f(2a − x) = −f(x), prove that
If f is an integrable function, show that
\[\int\limits_{- a}^a f\left( x^2 \right) dx = 2 \int\limits_0^a f\left( x^2 \right) dx\]
Evaluate each of the following integral:
If \[f\left( x \right) = \int_0^x t\sin tdt\], the write the value of \[f'\left( x \right)\]
If \[\int\limits_0^1 f\left( x \right) dx = 1, \int\limits_0^1 xf\left( x \right) dx = a, \int\limits_0^1 x^2 f\left( x \right) dx = a^2 , then \int\limits_0^1 \left( a - x \right)^2 f\left( x \right) dx\] equals
\[\int\limits_{- \pi/2}^{\pi/2} \sin^9 x dx\]
\[\int\limits_0^{\pi/2} \frac{\sin^2 x}{\sin x + \cos x} dx\]
Evaluate the following:
`int_0^oo "e"^(-mx) x^6 "d"x`
Evaluate `int sqrt((1 + x)/(1 - x)) "d"x`, x ≠1
Evaluate the following:
`int ((x^2 + 2))/(x + 1) "d"x`
