Advertisements
Advertisements
प्रश्न
पर्याय
\[\frac{- x^4}{4} + C\]
\[\frac{\left| x \right|^4}{4} + C\]
\[\frac{x^4}{4} + C\]
none of these
Advertisements
उत्तर
none of these
\[\int \left| x \right|^3 dx\]
\[\left| x \right| = \begin{cases}x,& x \geq 0\\ - x,& x < 0\end{cases}\]
Case 1 :-
\[\text{When }x \geq 0\]
\[ \therefore \int \left| x \right|^3 dx\]
\[ = \int x^3 dx\]
\[ = \frac{x^4}{4} + C\]
Case 2 :-
\[x < 0\]
\[\int \left| x \right|^3 dx\]
\[ = - \int x^3 dx\]
\[ = \frac{- x^4}{4} + C\]
APPEARS IN
संबंधित प्रश्न
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
`int sqrt(1+ x^2) dx` is equal to ______.
Evaluate : `int_2^3 3^x dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find `int (dx)/sqrt(4x - x^2)`
What is a standard integral?
Evaluate \[\int \frac{dx}{x^2+a^2}\].
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
Evaluate \[\int\frac{dx}{x^2-6x+13}\].
What is the completed-square form of \[3x^2+13x-10\]?
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
