Check the solution to "Evaluate the integral. ∫(8s3−12s2+5)ds"

sputavanomr

Answered question

2021-11-07

Evaluate the integral.

\int (8 s^{3} - 12 s^{2} + 5) d s

George Woody

Beginner2021-11-08Added 16 answers

Step 1
To Determine: evaluate the integral
Given: we have an integral

\int (8 s^{3} - 12 s^{2} + 5) d s

Explanation: we have an integral

\int (8 s^{3} - 12 s^{2} + 5) d s

now we know that the integral

\int x^{n} d x = \frac{x^{n + 1}}{n + 1}

here we will integrate with respect to ds so we have
Step 2

8 \int s^{3} d s - 12 \int s^{2} d s + 5 \int d s = 8 \frac{s^{3 + 1}}{3 + 1} - 12 \frac{s^{2 + 1}}{2 + 1} + 5 s

= \frac{8}{4} s^{4} - \frac{12}{3} s^{3} + 5 s

= 2 s^{4} - 4 s^{3} + 5 s + C

Answer: we have

\int (8 s^{3} - 12 s^{2} + 5) d s = 2 s^{4} - 4 s^{3} + 5 s + C

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