Help to Integral Calculus Solutions & Examples

Evaluate the integral.
${\displaystyle {\int }_{\frac{\pi }{4}}^{\frac{3\pi }{4}}8{\csc }^{2}xdx}$

Find the indefinite integral.
${\displaystyle \int e^{-0.05t}dt}$

a)
To simplify:
The radical expression ${\displaystyle \sqrt{20}}$

To convert the given radical expression $\sqrt[4]{5^2}$ to its rational exponent form and then simplify

To convert the given radical expression $\sqrt[4]{9}\sqrt{3}$ to its rational exponent form and then simplify

Evaluate the definite integral.
${\displaystyle {\int }_0^1{x}^3{(2x^4+1)}^{2}dx}$

Find the indefinite integral.
${\displaystyle \int (\frac{3}{t}-\frac{2}{t^2})dt}$

Evaluate the integral.
${\displaystyle \int {\sec h}^{2}w\tan hwdw}$

Mass Analysis of Two Chlorine-Fluorine Samples SampleMass of Chlorine (g)Mass of Fluorine (g)% Cl% F I13.0226.97865.1134.89 II5.7539.248??
Which statement best describes the relationship between the two samples?
A. The compound in Sample I is the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of definite proportions.
B. The compound in Sample I is the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of multiple proportions.
C. The compound in Sample I is not the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of definite proportions.
D. The compound in Sample I is not the same as in Sample II. Therefore, the mass ratio of Cl to F in both samples will obey the law of multiple proportions.

To find:
The value of ${\displaystyle \underset{x\to 0}{lim}\left(\frac{4^{3x}-4^x}{4^x-1}\right)}$ if it exists. If limit does not exist , then find out if one-sided limit exists.

To fill: The missing form of the expression

Evaluate the integrals
${\displaystyle {\int }_{-2}^{-1}{e}^{-(x+1)}dx}$

Evaluate each expression.
P(14,0)

Find the indefinite integral.
${\displaystyle \int \sin 2x\cos 2xdx}$

Сalculate the integral.
${\displaystyle \int x\sin h(x^2+1)dx}$

The integrals converge. Evaluate the integrals without using tables.
${\displaystyle {\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{2xdx}{{(x^2+1)}^2}}$

Find the indefinite integral.
${\displaystyle \int {\csc }^2\left(\frac{x}{2}\right)dx}$

Find integral.
${\displaystyle \int x\sqrt{1-4x^2}dx}$

Find the indefinite integral.
${\displaystyle \int \frac{6}{z\sqrt{9z^2-25}}}$

Evaluate the indefinite integral.
${\displaystyle \int {(4-x^3)}^{2}dx}$