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

Answer 1

There is a lot work that you posted here. I show how to start #1 which will give you the basics of using substitution for integration. Try to understand that one and see if you can progress from there. It might be that you need to schedule a lesson.

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https://latex.codecogs.com/svg.image?\begin{align*}&space;\int_{1}^{\sqrt{2}}\frac{4x^3}{3+x^4}dx&space;\\&space;\\let\\&space;&space;u&=3+x^4&space;\\&space;&space;du&=4x^3&space;dx&space;\\&space;\\now&space;\&space;integral&space;\&space;can&space;\&space;written&space;\&space;in&space;\&space;this&space;\&space;form:&space;\\&space;\int_{}^{}\frac{du}{u}&space;&=&space;\ln&space;u\\&space;\end{align*}&space;