Learn Integrals with Examples and Practice Problems

Evaluate the line integral, where C is the given curve.C $y^{3} d s, C : x = t^{3}, y = t, 0 \leq t \leq 5$

pancha3 2021-05-17

Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)
$7 \sin^{8} (x) \cos (x) \ln (\sin (x)) d x$

no. 101. $\int u^{n} \ln u d u = \frac{u^{n + 1}}{{(n + 1)}^{2}} [(n + 1) \ln u - 1] + C$

avissidep 2021-05-16

Find the exact length of the curve.
$y = \sqrt{x - x^{2}} + \sin^{- 1} \sqrt{x}$

Lewis Harvey 2021-05-16

Find the area of the part of the plane $5 x + 3 y + z = 15$ that lies in the first octant.

Clifland 2021-05-14

a) Write the sigma notation formula for the right Riemann sum $R_{n}$ of the function $f (x) = 4 - x^{2}$ on the interval $[0, 2]$ using n subintervals of equal length, and calculate the definite integral $\int_{0}^{2} f (x) d x$ as the limit of $R_{n}$ at $n \to \infty$ .
(Reminder: $\sum_{k = 1}^{n} k = \frac{n (n + 1)}{2}, \sum_{k = 1}^{n} k^{2} = \frac{n (n + 1) (2 n + 1)}{6}$
b) Use the Fundamental Theorem of Calculus to calculate the derivative of $F (x) = \int_{e^{- x}}^{x} \ln (t^{2} + 1) d t$

Nann 2021-05-14

Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)
$\int 37 e^{74 x} \arctan (e^{37 x}) d x$
Inverse Trigonometric Forms (92): $\int u \tan^{- 1} u d u = \frac{u^{2} + 1}{2} \tan^{- 1} u - \frac{u}{2} + C$

coexpennan 2021-05-12

Calculate the double integral.
$\int \int_{R} \frac{4 x}{1 + x y} d A$
$R = [0, 4] \times [0, 1]$

Cem Hayes 2021-05-12

Solved by the radical integration.
$\int \frac{\sqrt{1 - x^{2}}}{x^{4}} d x$

ringearV 2021-05-04

Evaluate the definite integral.
$\int_{0}^{1} \sqrt[3]{1 + 7 x} d x$

sjeikdom0 2021-03-09

Evaluate the following integrals.
$\int_{0}^{1} \frac{16^{x}}{4^{2 x}} d x$

djeljenike 2021-03-02

Evaluate the following iterated integrals.
$\int_{0}^{3} \int_{- 2}^{1} (2 x + 3 y) d x d y$

York 2021-02-25

Evaluate the following iterated integrals.
$\int_{0}^{2} \int_{0}^{1} 4 x y d x d y$

aortiH 2021-02-25

Evaluate the following definite integrals.
$\int_{5}^{3 \sqrt{5}} \frac{d x}{\sqrt{x^{2} - 9}}$

Chaya Galloway 2021-02-24

Evaluate the following integrals.
$\int x^{2} 10^{x^{3}} d x$

coexpennan 2021-02-22

Evaluate the following integrals. Include absolute values only when needed.
$\int 3^{- 2 x} d x$

nicekikah 2021-02-14

Evaluate the following integrals.
$\int \frac{e^{\sin x}}{\sec x} d x$

aflacatn 2021-02-12

Evaluate the following integrals.
$\int_{0}^{3} \frac{2 x - 1}{x + 1}$

glasskerfu 2021-02-06

Evaluate the following integrals.
$\int_{- 1}^{1} 10^{x} d x$

Bevan Mcdonald 2021-02-06

Evaluate the following integrals.
$\int_{0}^{\frac{π}{2}} 4^{\sin x} \cos x d x$

Kye 2021-01-31

Evaluate the following iterated integrals.
$\int_{0}^{2} \int_{0}^{1} \frac{8 x y}{1 + x^{4}} d x d y$

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Calculus 1

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