Find the value of _ -4 ^4|x| d x. - Vidyadip

Question

Find the value of $\int_{-4}^4|x| d x$.

✓

Answer

Let $ I =\int_{-4}^4|x| d x=\int_{-4}^0|x| d x+\int_0^4|x| d x$
$ \because|x|=\left\{\begin{array}{l} x, x>0 \\ -x, x<0\end{array}\right.$
$\therefore =\int_{-4}^0 - x\ d x+\int_0^4 x\ d x$
$ =\left(\frac{-x^2}{2}\right)_{-4}^0+\left(\frac{x^2}{2}\right)_0^4$
$ =\frac{-1}{2}(0-16)+\frac{1}{2}(16-0)$
$=8+8$
$=16$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from Integrals→Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the value of $k$ so that the function $f$ is continuous at the indicated point:
$f(x)=\left\{\begin{array}{c}k x^2, \text { if } x \leq 2 \\ 3, \text { if } x>2\end{array}\right.$ at $x=2$.

Integrate the function x log 2x

If A, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P(A) + P(B) + P(C).

Determine order and degree $($if defined$)$ of differential equations given in Exercise.
$(y''')^2 + (y")^3 + (y')^4 + y^5 = 0$

Find the value of $\int(1+x)\left(1+x^2\right)(1-x) d x$ :

Find the principal value of $\sec^{-1}( {\frac{2}{{\sqrt 3 }}} )$.

Classify the following as scalar and vector quantities:
Velocity.

Find the direction cosines of the vector $\hat{i}+2\hat{j}+3\hat{k}.$

Evaluate the following:
$\cot^{-1}\Big(\cot\frac{\pi}{3}\Big)$

Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find P(A or B).