Mathematics

# Evaluate the integral $\displaystyle\int_{-4}^{4}|x+2|\ dx$.

##### SOLUTION
$\displaystyle\int_{-4}^{4}|x+2|\ dx=\displaystyle\int_{-4}^{-2}-(x+2)\ dx+\int_{-2}^{4}(x+2) dx=\left[\dfrac{-x^{2}}{2}-2x\right]_{-4}^{-2}+\left[\dfrac{x^{2}}{2}+2x\right]_{-2}^{4}$

$=\dfrac {-4}{2}+4-\dfrac {16}2-8+\dfrac {16}2+8-\dfrac 42+4=-2+4-16+16-2+4=4$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
$\int {\cot xdx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\int {\dfrac{{\sin x + \cos x}}{{\sqrt {\sin 2x} }}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^1_0\dfrac{2x}{(1+x^4)}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The function $f\left( x \right) =\displaystyle\int _{ 0 }^{ x }{ \log { \left( \dfrac { 1-x }{ 1+x } \right) } dx }$
• A. An odd function
• B. A periodic function
• C. None of these
• D. An even function

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$