Learn Integrals with Examples and Practice Problems

We want to find the exact length of the arc along the curve $y = 1 + 6 x^{3 / 2}$ from (0,0) to (4,49)
a) Set up the integral that will calculate the arc length.
b)L=?
b) Evaluate the integral exactly.
L=?
c) Use your calculator and approximate the arc length correct to three decimals.
$L \approx ?$

experimediaisF 2022-11-26

Integers are closed under division, i.e. for any two integers, a and b, a/b will be an integer. True or false.

Goundoubuf 2022-11-25

Use the Fundamental Theorem of Calculus to calculate the definite integral. Give an exact answer
$\int_{0}^{\frac{π}{2}} e^{\cos θ} \sin θ d θ$

blogmarxisteFAu 2022-11-25

Integral $\cos (2 θ)$ ?

nonhumanWd3 2022-11-25

Knowing that: $\int e^{k x} d x = \frac{1}{k} e^{k x} + c$ show that $\int a^{x} d x = \frac{1}{\ln a} \cdot a^{x} + c$

Scarlet Marshall 2022-11-24

Evaluate the line integral, where C is the given curve.
$\int_{C} x y d s, C : x = t^{2}, y = 2 t, 0 \leq t \leq 3$
thanks show all work and steps

ingerentayQL 2022-11-24

Let C be the curve of intersection of the parabolic cylinder $x^{2} = 2 y$ , and the surface $3 z = x y$ . Find the exact length of C from the origin to the point (2, 2, 4/3).

Jamie Medina 2022-11-24

Use a double integral to find the volume of the indicated solid. $z = 1 - x y, y = x, y = 1$

Talia Frederick 2022-11-23

If $f (x) = e^{- x} + 2 e^{- 2 x} + 3 e^{- 3 x} + \dots$ then find $\int_{\ln 2}^{\ln 3} f (x) d x$

Jamie Medina 2022-11-22

Need a hint to evaluate the indefinite integral $\int \frac{e^{x} (2 - x^{2})}{(1 - x) \sqrt{1 - x^{2}}} d x$

Demarion Ortega 2022-11-20

Prove $\int_{0}^{\infty} \frac{\sin^{4} x}{x^{4}} d x = \frac{π}{3}$

Elliana Molina 2022-11-20

Evaluate
$\int_{0}^{1} (x^{5} + x^{4} + x^{2}) \sqrt{4 x^{3} + 5 x^{2} + 10} d x$

Melissa Walker 2022-11-19

Integral inequality: $\frac{1}{30} < \int_{2}^{\infty} \frac{\sqrt{s^{3} - s^{2} + 3}}{s^{5} + s^{2} + 1} d s < \frac{\sqrt{2}}{20}$

trumansoftjf0 2022-11-18

I want to calculate
$\int_{C^{+} (2, 2)} \frac{e^{\sqrt{z}}}{(z - 2)^{2}} d z and \int_{0}^{\infty} \frac{1}{1 + x \sqrt{x}} d x$

Mark Rosales 2022-11-12

Integral of a rational function
$\int \frac{\sqrt[3]{x} + 1}{\sqrt[4]{x^{3}} (\sqrt{x} - \sqrt[6]{x}) d x}$

Jorge Schmitt 2022-11-12

How can I tell if this integral converges or not?
$\int_{0}^{\infty} \frac{e^{x}}{x^{x}} d x$

klasyvea 2022-11-10

Evaluate $\int \frac{\sin^{- 1} \sqrt{x}}{\sqrt{1 - x}} d x$

ajakanvao 2022-11-10

How would one go about integrating the following?
$\int_{0}^{5} \frac{x}{x - 2} d x$

inurbandojoa 2022-11-10

Evaluate the integral:
$\int_{- 1}^{1} \frac{x^{2}}{2} d x$

Paula Cameron 2022-11-09

Solve this integral:
$\int \frac{1}{16 + x^{2}} d x$

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Calculus 1

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