Question

plzz find the area under the curve of function 3^(2x+1)^0.5 from x=0 to x=4

Answer 1

integral

Answer 2

I understand it's \[3^{\sqrt{2x+1}}\]
Substitute \[2x+1 =y^2\]
Differentiate both sides and you will get a equation in terms of y.
Adjust the limits accordingly and integrate.
I believe you will get \[2\int\limits_{?}^{?}3^{y}ydy\]
Resubstitute on finding the integral.

Answer 3

\[\int\limits_0^4 3^{\sqrt{1+2 x}} \, dx=\frac{-24+78 \text{Log}[3]}{\text{Log}[3]^2}=51.1138 \]Plot attached.