Evaluate the following using The Substitution Rule and the Fundamental Theorem of Calculus.

Question

Evaluate the following using The Substitution Rule and the Fundamental Theorem of Calculus.

Problems is on this image

image- https://imgur.com/9qB5VSG

complete solution of 3 and 4

Answer 1

The e^x's will cancel out and you can pull out the resulting 5.

∫_-ln3^ln3 ( e^x/e^x + 4 )dx = 5 ∫_-ln3^ln3 dx = 5 ( ln3 - ( - ln3 ) ) = 5 ( 2 ln 3 )

∴ ∫_-ln3^ln3 ( e^x/e^x + 4 )dx = 10 ln 3 ≈ 10.986

I hope this helps! Message me in the comments with any questions, comments, or concerns!