Question

Whats the value of y ?


`\displaystyle{ \qquad \sf \: y = \sf \int _0 }^(1) \sf (x {}^(2) + 5)\: \: dx`
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Answer 1

Refer to the photo taken.

Answer 2

5 1/3

Explanation:

You want the value of the definite integral of (x² +5) on the interval [0, 1].

Integral

The power rule applies:

∫(x^n)dx = (x^(n+1))/(n+1)

This means the integral is ...

`\displaystyle \int_0^1{(x^2+5)}\,dx=\left((x^3)/(3)+5x\right)_0^1=(1)/(3)+5`

The value of y is 5 1/3.