Evaluate the iterated integral:

a)

b)

c)

d)

rocedwrp
2021-09-02
Answered

Evaluate the iterated integral:

a)

b)

c)

d)

You can still ask an expert for help

2abehn

Answered 2021-09-03
Author has **88** answers

a)

b)

c)

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a) Write the sigma notation formula for the right Riemann sum $R}_{n$ of the function $f\left(x\right)=4-{x}^{2}$ on the interval $[0,\text{}2]$ using n subintervals of equal length, and calculate the definite integral ${\int}_{0}^{2}f\left(x\right)dx$ as the limit of $R}_{n$ at $n\to \mathrm{\infty}$ .

(Reminder:$\sum _{k=1}^{n}k=n\frac{n+1}{2},\text{}\sum _{k=1}^{n}{k}^{2}=n(n+1)\frac{2n+1}{6})$

b) Use the Fundamental Theorem of Calculus to calculate the derivative of$F\left(x\right)={\int}_{{e}^{-x}}^{x}\mathrm{ln}({t}^{2}+1)dt$

(Reminder:

b) Use the Fundamental Theorem of Calculus to calculate the derivative of

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I've been learning the fundamental theorem of calculus. So, I can intuitively grasp that the derivative of the integral of a given function brings you back to that function. Is this also the case with the integral of the derivative? And if so, can you please give a intuition for why this is true? Tha

in advance

I've been learning the fundamental theorem of calculus. So, I can intuitively grasp that the derivative of the integral of a given function brings you back to that function. Is this also the case with the integral of the derivative? And if so, can you please give a intuition for why this is true? Tha

in advance