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Calculus and Analysis
Differential Calculus
Analyzing functions

impresijuzj

Answered question

2021-11-30

Sketch the graphs of the functions.

f (x) = x^{3} + x^{2} - 2 x and g (x) = 0

Find the ares of the rezion completely enclosed by the graphs of the given functions fand g.

Answer & Explanation

Melinda Olson

Beginner2021-12-01Added 20 answers

Step 1
Sketch the region:

Step 2
Ares between the curves,
$A = \int_{a}^{b} ∣ f (x) - g (x) ∣ d x$
Equating two functions,
$X^{3} + x^{2} - 2 x = 0$
Solve,
$x = - 2, x = 1$ .
$A = \int_{- 2}^{1} ∣ x^{3} + x^{2} - 2 ∣ d x$
Eliminate absolute,
$A = \int_{- 2}^{0} x^{3} + x^{2} - 2 x d x + \int_{0}^{1} - x^{3} - x^{2} + 2 x d x$
Now integrate the term,
$A = \frac{8}{3} + \frac{5}{12} = \frac{37}{12}$
Thus area between the curve is $A = \frac{37}{12}$

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