CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration of Piecewise Continuous Functions

Evaluate the ...

Question

Evaluate the following:
$\int_{- 4}^{4} | x + 2 | d x$

Open in App

Solution

Consider, $I = \int_{- 4}^{4} | x + 2 | d x$

$I = \int_{- 4}^{- 2} - (x + 2) d x + \int_{- 2}^{4} (x + 2) d x$

$I = {[\frac{- x^{2}}{2} - 2 x]}_{- 4}^{- 2} + {[\frac{x^{2}}{2} + 2 x]}_{- 2}^{4}$

$I = \frac{- 4}{2} + 4 - \frac{16}{2} - 8 + \frac{16}{2} + 8 - \frac{4}{2} + 4$

$I = - 2 + 4 - 16 + 16 - 2 + 4 = 4$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Evaluate the following integrals:

\int_{- 4}^{4} |x + 2| d x

Q. Evaluate the following integrals:

\int \frac{x^{2}}{(x^{2} + a^{2}) (x^{2} + b^{2})} d x

Q. Evaluate the following integrals:

\int e^{2 x} \sin (3 x + 1) d x

Q. Evaluate the following integrals:

\int_{- 5}^{0} f (x) d x, where f (x) = |x| + |x + 2| + |x + 5|

4 \int - 4 | x + 2 | d x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Integration of Piecewise Functions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Integration of Piecewise Continuous Functions

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon