Step by step solution to "Combine the integrals into one integral, then evaluate..."

ringearV

Answered question

2021-11-07

Combine the integrals into one integral, then evaluate the integral.

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

Khribechy

Skilled2021-11-08Added 100 answers

Step 1
Given integral is

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

Step 2
On solving

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

= \int (x^{3} + x^{2}) + (x^{3} + x^{2}) d x

= \int 2 (x^{3} + x^{2}) d x

= 2 [\frac{x^{4}}{4} + \frac{x^{3}}{3}] + C [\int x^{n} d x = \frac{x^{n + 1}}{n + 1}]

= \frac{x^{4}}{2} + \frac{2 x^{3}}{3} + C

where C is integration constant.

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