Advertisements
Advertisements
Question
\[\int\limits_0^2 \left( 2 x^2 + 3 \right) dx\]
Advertisements
Solution
\[\int_0^2 \left( 2 x^2 + 3 \right) d x\]
\[ = \left[ \frac{2 x^3}{3} + 3x \right]_0^2 \]
\[ = \frac{16}{3} + 6 = \frac{34}{3}\]
APPEARS IN
RELATED QUESTIONS
Prove that:
Evaluate each of the following integral:
The value of \[\int\limits_{- \pi}^\pi \sin^3 x \cos^2 x\ dx\] is
The value of \[\int\limits_{- \pi/2}^{\pi/2} \left( x^3 + x \cos x + \tan^5 x + 1 \right) dx, \] is
\[\int\limits_0^1 \cos^{- 1} x dx\]
\[\int\limits_0^{\pi/2} x^2 \cos 2x dx\]
\[\int\limits_0^{\pi/4} \tan^4 x dx\]
\[\int\limits_0^{\pi/2} \left| \sin x - \cos x \right| dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \cot^7 x} dx\]
\[\int\limits_0^\pi \frac{x \sin x}{1 + \cos^2 x} dx\]
\[\int\limits_0^\pi \frac{x \tan x}{\sec x + \tan x} dx\]
\[\int\limits_2^3 e^{- x} dx\]
Using second fundamental theorem, evaluate the following:
`int_1^2 (x - 1)/x^2 "d"x`
Evaluate the following integrals as the limit of the sum:
`int_0^1 (x + 4) "d"x`
Choose the correct alternative:
Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is
Evaluate `int sqrt((1 + x)/(1 - x)) "d"x`, x ≠1
Find `int x^2/(x^4 + 3x^2 + 2) "d"x`
