Get Your Calculus 1 Questions Answered Here!

Prove that:
$\int_{0}^{\frac{π}{2}} \ln^{2} (\cos x) d x = \frac{π}{2} \ln^{2} 2 + \frac{π^{3}}{24}$

Arthur Pratt 2021-12-31

Is there a general formula for finding the primitive of
$e^{a x} \sin (b x)$

Brock Brown 2021-12-31

It is possible to prove that
$\int_{0}^{\infty} \frac{e^{i x} - e^{- x}}{x} d x = - i \frac{π}{2}$

eiraszero11cu 2021-12-31

I am looking for a short proof that
$\int_{0}^{\infty} {(\frac{\sin x}{x})}^{2} d x = \frac{π}{2}$
What do you think?

piarepm 2021-12-31

Suppose that we do not know anything about the complex analysis (numbers). In this case, how to calculate the following integral in closed form?
$\int_{0}^{\infty} \frac{\cos x}{1 + x^{2}} d x$

compagnia04 2021-12-31

How to prove
$\int_{0}^{\infty} e^{- x^{2}} d x = \frac{\sqrt{π}}{2}$

David Lewis 2021-12-30

I have a real valued number $y_{t}$ . At each time step t, $y_{t}$ is multiplied by $(1 + ϵ)$ with probability p and multiplied by $(1 - ϵ)$ with probability $1 - p$ . What is the expected value of $y_{t + n}$ ? What is the variance?

Lennie Davis 2021-12-30

How to evaluate:
$\int_{- \infty}^{\infty} \frac{\ln (x^{2} + 1)}{x^{2} + 1} d x$

kuhse4461a 2021-12-30

How can you evaluate
$\int_{0}^{\frac{π}{2}} \log \cos (x) d x$ ?

piarepm 2021-12-30

Evaluate the integral $\int_{0}^{\frac{π}{2}} \frac{\sin^{3} x}{\sin^{3} x + \cos^{3} x} d x$

zakinutuzi 2021-12-30

Solve integrals using residue theorem?
$\int_{0}^{π} \frac{d θ}{2 + \cos θ}$
$\int_{0}^{\infty} \frac{x}{{(1 + x)}^{6}} d x$

Roger Smith 2021-12-30

I have to calculate this integrals
$I_{1} = \int_{0}^{2} \frac{\arctan (x)}{x^{2} + 2 x + 2} d x$
$I_{2} = lim_{n \to \infty} \int_{0}^{n} \frac{\arctan x}{x^{2} + x + 1} d x$
I have a hint on the first one, the substitution $x = \frac{2 - t}{1 + 2 t}$ , but I can't understand how it was conceived.

William Burnett 2021-12-30

What is the derivative of $5^{x}$ ?

Shirley Thompson 2021-12-30

Find all the second partial derivatives. $v = \frac{x y}{x - y}$

Harold Kessler 2021-12-27

Let $f (x) = \frac{{(x + 8)}^{2}}{x^{2} - 64}$ . Find a) $lim_{x \Rightarrow - 8} f (x)$ , b) $lim_{x \Rightarrow 0} f (x)$ , and c) $lim_{x \Rightarrow 8} f (x)$ .

Marla Payton 2021-12-26

How do you find the antiderivative of $\cos^{2} (x)$ ?

chezmarylou1i 2021-12-23

Show the steps needed to find the given solutions.
$\int \frac{\arctan c}{1 + x^{2}} d x$

eliaskidszs 2021-12-23

Find the cubic function $f (x) = a x^{3} + b x^{2} + c x + d$ that has a local maximum value of 3 at $x = - 2$ and a local minimum value of 0 at $x = 1$ .

quiquenobi2v6 2021-12-22

If $x^{2} + x y + y^{3} = 1$
find the value of y

oliviayychengwh 2021-12-21

What is the integral of 0?
I am trying to convince my friend that the integral of 0 is C, where C is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is 0.

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.

Calculus 1

Master Calculus 1 Practice Problems with Expert Help