Expert answers to "Compute, please, definite integral which have a absolute..."

High School
Calculus and Analysis
Calculus 1
Integrals

ushwaui

Answered question

2021-11-19

Compute, please, definite integral which have a absolute value function like these below:

\int_{- 2}^{3} | x | d x

\int_{- 2}^{3} | x - 1 | d x

\int_{- 2 π}^{2 π} | \sin x | d x

Answer & Explanation

Elizabeth Witte

Beginner2021-11-20Added 24 answers

You should consider the fact that |x| is one linear function for $x \in (- \infty; 0]$ and a linear function for $x \in [0; \infty)$ to break the interval of integration into subintervals that are easier.
$\int_{- 2}^{3} | x | d x = \int_{- 2}^{0} - x d x + \int_{0}^{3} x d x$

Crom1970

Beginner2021-11-21Added 6 answers

Firstly, you can split each integral into multiple, smaller integrals for your first integral, such as:

\int_{- 2}^{0} - x d x

and

\int_{0}^{3} x d x

You can also look at the graphs and calculate the area underneath them using simple geometry.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f (x, y) = x^{3} - 6 x y + 8 y^{3}$
$\frac{1}{\sec (x)}$ in derivative?
What is the derivative of $\ln (x + 1)$ ?
What is the limit of $e^{- x}$ as $x \to \infty$ ?
What is the derivative of $f (x) = 5^{\ln x}$ ?
What is the derivative of $e^{- 2 x}$ ?
How to find $lim \frac{e^{t} - 1}{t}$ as $t \to 0$ using l'Hospital's Rule?
What is the integral of $\sqrt{9 - x^{2}}$ ?
What is the derivative of $f (x) = \ln [x^{9} {(x + 3)}^{6} {(x^{2} + 7)}^{5}]$ ?
What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?
How to find the derivative of $y = e^{5 x}$ ?
How to evaluate the limit $\frac{\sin (5 x)}{x}$ as x approaches 0?
How to find derivatives of parametric functions?
What is the antiderivative of $- 5 e^{x - 1}$ ?
How to evaluate: indefinite integral $\frac{1 + x}{1 + x^{2}} d x$ ?

Didn't find what you were looking for?