What is the integral from 0 to 3 of 3^x+sqrt(9-x^2) ?

The integral from 0 to 3 of 3^x+sqrt(9-x^2) is (26}{ln(3)}+\frac{9pi)/4

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integral from 0 to 3 of 3^x+sqrt(9-x^2)

\int_{0}^{3} 3^{x} + 9 - x^{2} d x

\frac{26}{ln ( 3 )} + \frac{9 π}{4}

Decimal Notation

30.73480 \dots

Solution steps

\int_{0}^{3} 3^{x} + 9 - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{3} 3^{x} d x + \int_{0}^{3} 9 - x^{2} d x

\int_{0}^{3} 3^{x} d x = \frac{26}{ln ( 3 )}

\int_{0}^{3} 9 - x^{2} d x = \frac{9 π}{4}

= \frac{26}{ln ( 3 )} + \frac{9 π}{4}

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What is the integral from 0 to 3 of 3^x+sqrt(9-x^2) ?
The integral from 0 to 3 of 3^x+sqrt(9-x^2) is (26}{ln(3)}+\frac{9pi)/4