Evaluate the following definite integral: $\int_{-3}^3(3x + 5)\,dx$ I'm new to the topic of integration and I'm struggling big time with it.
I am trying to evaluate $\int_{-3}^3(3x + 5)\,dx$.
Any help is greatly appreciated.
Thank you

Have you learned the Fundamental Theorem of Calculus yet?
If so, recall that you can evaluate definite integrals of $3x + 5$ using an antiderivative. In particular
$$
\int_{-3}^3 3x + 5 \,dx = \left[\frac{3}{2}x^2 + 5x \right]_{-3}^3
$$
Otherwise, you should draw a graph of this function and use simple geometry to find the integral - recall that the integral is related to the area between the function and the $x$-axis; if the area is above the $x$-axis, you count it positively, and if it is below, you count it negatively.
Further, because this function is so basic, you'll be able to calculate the areas involved using simple geometric formulae for triangles.

