Get Your Calculus 1 Questions Answered Here!

Proof that:
$\int_{0}^{\frac{π}{2}} \ln (1 + α \sin^{2} x) d x = π \ln \frac{1 + \sqrt{1 + α}}{2}$

Concepcion Hale 2022-01-03

Evaluate integral:
$\int_{0}^{\frac{π}{3}} \ln^{2} (\frac{\sin x}{\sin (x + \frac{π}{3})}) d x$

Ernest Ryland 2022-01-03

How to integrate
$\frac{\cos (7 x) - \cos (8 x)}{1 + 2 \cos (5 x)}$

Francisca Rodden 2022-01-03

Show that:
$\int_{0}^{\infty} \frac{\sin^{3} (x)}{x^{3}} d x = \frac{3 π}{8}$

Lennie Davis 2022-01-03

How can I prove that?
$\int_{0}^{1} \frac{\ln (x)}{x^{2} - 1} d x = \frac{π^{2}}{8}$

sunshine022uv 2022-01-03

Find out
$\int e^{\cos x} d x$

Algotssleeddynf 2022-01-02

How to compute the following integral?
$\int \log (\sin x) d x$

osula9a 2022-01-02

Calculate:
$\int_{0}^{\infty} \frac{\ln^{2} (x)}{{(1 - x^{2})}^{2}} d x$

Irvin Dukes 2022-01-02

How would I go about evaluating this integral?
$\int_{0}^{\infty} \frac{\ln (x^{2} + 1)}{x^{2} + 1} d x$

Charles Kingsley 2022-01-02

How can I find the principal value of the following?
$P V \int_{- \infty}^{\infty} \frac{e^{i x}}{x (x^{2} + x + 1)} d x$

kloseyq 2022-01-02

The question is: using the comparison test for improper integrals state if
$\int_{0}^{\infty} x^{4} e^{- x} d x$ converges or not.

veksetz 2022-01-02

Double Integrals involving infinity
$\int_{0}^{\infty} \int_{0}^{\infty} x y e^{- (x^{2} + y^{2})} d x d y$

Ernest Ryland 2022-01-01

Sovle integral:
$\int_{0}^{\infty} \log (1 + x^{2}) \frac{cosh \frac{π x}{2}}{{sinh}^{2} \frac{π x}{2}} d x = 2 - \frac{4}{π}$

Wanda Kane 2022-01-01

How would you compute the following integrals?
$I_{n} = \int_{0}^{π} \frac{1 - \cos n x}{1 - \cos x} d x$
$J_{n, m} = \int_{0}^{π} \frac{x^{m} (1 - \cos n x)}{1 - \cos x} d x$

Ashley Bell 2022-01-01

I want to solve these Integrals
1. $\int_{0}^{\frac{π}{2}} \frac{1}{1 + \tan^{\sqrt{2}} x} d x$
2. $\int_{0}^{\frac{π}{2}} \frac{1}{{(\sqrt{2} \cos^{2} x + \sin^{2} x)}^{2}}$

Deragz 2022-01-01

I need help calculating two integrals
1) $\int_{1}^{2} \sqrt{4 + \frac{1}{x}} d x$
2) $\int_{0}^{\frac{2}{π}} x^{n} \sin (x) d x$

Joseph Krupa 2022-01-01

How to calculate the value of the integrals
$\int_{0}^{1} {(\frac{\arctan x}{x})}^{2} d x$ ,
$\int_{0}^{1} {(\frac{\arctan x}{x})}^{3} d x$
and $\int_{0}^{1} \frac{\arctan^{2} x \ln x}{x} d x$ ?

zakinutuzi 2021-12-31

Furthermore why is it that $e^{x}$ is used in exponential modelling? Why aren't other exponential functions used, i.e. $2^{x}$ , etc?

expeditiupc 2021-12-31

What is the derivative of $y = \arctan (x)$ ?

Krzychau1 2021-12-31

Show that $\int_{1}^{2} \frac{e^{x} (x - 1)}{x (x + e^{x})} d x = \ln (\frac{2 + e^{2}}{2 + 2 e})$ and $\int_{0}^{\frac{π}{2}} \frac{x \sin (2 x)}{1 + {\cos (2 x)}^{2}} d x = \frac{π^{2}}{16}$

The majority of Calculus 1 questions and answers that you will find below should be sufficient for understanding the basic rules that are necessary for problem-solving purposes. Take a look at the original answers, seek math assignment help, and compare them to what you have for your assignment.

If you need any other kind of help for your Calculus 1 tasks, combine several solutions or look at the problem that seems similar to your original assignment. If Math is not your subject per se, start with the most basic problems and proceed with the complex ones.

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