There is a formula for calculating the integral of xn for any n. It is ∫abxndx=1n+1bn+1−1n+1an+1 So, substituting in n=7n=7, we find that ∫abx7dx=18b8−18a8 Note that this seems a bit too easy so if you haven't gotten to this formula in your class yet and you need to evaluate this integral using the definition or by "guessing" the antiderivative instead of using this rule directly, let me know in a comment and I'll update my answer.

Find out the answer to "∫bax7dx"

College
Calculus and Analysis
Integral Calculus
Integrals

Wierzycaz

Answered question

2021-01-02

\int_{b}^{a} x^{7} d x

Answer & Explanation

Nola Robson

Skilled2021-01-03Added 94 answers

There is a formula for calculating the integral of $x^{n}$ for any n. It is
$\int_{a}^{b} x^{n} d x = \frac{1}{n + 1} b^{n + 1} - \frac{1}{n + 1} a^{n + 1}$
So, substituting in n=7n=7, we find that
$\int_{a}^{b} x^{7} d x = \frac{1}{8} b^{8} - \frac{1}{8} a^{8}$
Note that this seems a bit too easy so if you haven't gotten to this formula in your class yet and you need to evaluate this integral using the definition or by "guessing" the antiderivative instead of using this rule directly, let me know in a comment and I'll update my answer.

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