Advertisements
Advertisements
Question
Solution
\[\text{We have}, \]
\[I = \int_0^1 e^\left\{ x \right\} d x\]
\[\text{We know that}, \]
\[\left\{ x \right\} = x\text{, when }0 < x < 1\]
\[ \therefore I = \int_0^1 e^x d x\]
\[ = \left[ e^x \right]_0^1 \]
\[ = e^1 - e^0 \]
\[ = e - 1\]
APPEARS IN
RELATED QUESTIONS
\[\int\limits_1^4 f\left( x \right) dx, where f\left( x \right) = \begin{cases}7x + 3 & , & \text{if }1 \leq x \leq 3 \\ 8x & , & \text{if }3 \leq x \leq 4\end{cases}\]
The value of the integral \[\int\limits_0^{\pi/2} \frac{\sqrt{\cos x}}{\sqrt{\cos x} + \sqrt{\sin x}} dx\] is
If \[\int\limits_0^a \frac{1}{1 + 4 x^2} dx = \frac{\pi}{8},\] then a equals
The value of the integral \[\int\limits_{- 2}^2 \left| 1 - x^2 \right| dx\] is ________ .
Evaluate: \[\int\limits_{- \pi/2}^{\pi/2} \frac{\cos x}{1 + e^x}dx\] .
`int_0^(2a)f(x)dx`
\[\int\limits_0^1 \frac{1 - x}{1 + x} dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \cot^7 x} dx\]
\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]
Using second fundamental theorem, evaluate the following:
`int_0^1 "e"^(2x) "d"x`
Using second fundamental theorem, evaluate the following:
`int_1^2 (x "d"x)/(x^2 + 1)`
Evaluate `int (x^2"d"x)/(x^4 + x^2 - 2)`
