Question

Fundamental Theorem of Calculus and its application.​

Answer 1

Explanation:

The fundamental theorem of calculus can be applied to the proper integrals. I'm going to use the general formula:

`\int\limits {x^n} \, dx =(x^n^+^1)/(n+1)`

I'm also going to assume you know the integrals of basic trig functions and 1/x. I cant prove them, you just have to know them.

a)
`y+(3y^2)/(2) -(y^4)/(4) +C`

b) ln|x| --> ln(6) - ln(3) = 0.69

c) sin(Ф) --> sin(2pi) - sin(0) = 0

d)
`2e^x` -->
`2e^l^n^(^6^)-2e^l^n^(^3^)=12-6=6`