Advertisements
Advertisements
Question
Options
−2
2
0
4
Advertisements
Solution
2
\[\int_{- 1}^1 \left| 1 - x \right| d x\]
\[ = \int_{- 1}^0 \left( 1 - x \right) dx + \int_0^1 \left( 1 - x \right) dx\]
\[ = \left[ x - \frac{x^2}{2} \right]_{- 1}^0 + \left[ x - \frac{x^2}{2} \right]_0^1 \]
\[ = 0 + 1 + \frac{1}{2} + 1 - \frac{1}{2} - 0\]
\[ = 2\]
APPEARS IN
RELATED QUESTIONS
Evaluate the following definite integrals:
\[\int\limits_0^{( \pi )^{2/3}} \sqrt{x} \cos^2 x^{3/2} dx\]
Evaluate the following integral:
If f (x) is a continuous function defined on [0, 2a]. Then, prove that
Evaluate each of the following integral:
\[\int\limits_0^1 \left\{ x \right\} dx,\] where {x} denotes the fractional part of x.
\[\int\limits_0^1 \tan^{- 1} x dx\]
\[\int\limits_0^{\pi/4} \sin 2x \sin 3x dx\]
\[\int\limits_0^1 \log\left( 1 + x \right) dx\]
Evaluate the following integrals :-
\[\int_2^4 \frac{x^2 + x}{\sqrt{2x + 1}}dx\]
\[\int\limits_0^{\pi/2} \left| \sin x - \cos x \right| dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \tan^3 x} dx\]
\[\int\limits_0^\pi \frac{x \sin x}{1 + \cos^2 x} dx\]
\[\int\limits_0^\pi x \sin x \cos^4 x dx\]
\[\int\limits_0^{\pi/2} \frac{x}{\sin^2 x + \cos^2 x} dx\]
Using second fundamental theorem, evaluate the following:
`int_1^"e" ("d"x)/(x(1 + logx)^3`
Using second fundamental theorem, evaluate the following:
`int_1^2 (x - 1)/x^2 "d"x`
Choose the correct alternative:
`int_0^oo "e"^(-2x) "d"x` is
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 the following:
`int ((x^2 + 2))/(x + 1) "d"x`
`int (x + 3)/(x + 4)^2 "e"^x "d"x` = ______.
Which integral has Constant C present?
