Master Calculus 1 Practice Problems with Expert Help

$y(x^2-1)dy+x(y^2+1)dx=0$

Check whether the given function is satisfying the Fubini’s theorem about ‎mixed partial derivative ‎
${\displaystyle f(x,y)=3x^2\sin \left(4xy\right)}$

${\int }_{0.2}^{2.2}x{e}^{x}dx$

Determine whether the expression is true or false:
${\displaystyle \int \tan \left(2x\right)\times dx=-\frac{1}{2}\ln \times \left|\cos \left(2x\right)\right|+C}$

$(1+e^x)ydy-e^{x}dx=0$

$\int \frac{x^2}{x}\frac{{(4+9x^2)}^1}{2}dx$

If ${\displaystyle f^{\left(n\right)}\left(0\right)=(n+1)!\text{ for }n=0,1,2,\dot{s}}$, find the Maclaurin series forf and its radius of convergence.

Please, find the integral ${\displaystyle \int \frac{10}{(x-1)(x^2+9)}dx}$

Use the method of reduction of order to find the general of the differential equation
$t(t+3)y{}^{″}-3(t+2)y^{\prime }+3y=0$

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, give the answer -1.
${\int }_4^{\mathrm{\infty }}x{e}^{-2x}$

how to find the derivative of ${\displaystyle f\left(u\right)=9e^u+20}$

${\int }_0^{a}3x^2\sqrt{a^2-x^2}dx$

Evaluate the iterated integral:
a) ${\displaystyle {\int }_0^3{\int }_0^{\frac{\pi }{3}}{\int }_0^{4}r\times \cos \theta drd\theta dz}$

b) ${\displaystyle {\int }_0^{\frac{\pi }{2}}{\int }_0^3{\int }_0^{4-z}zdrdzd\theta }$

c) ${\displaystyle {\int }_0^{\frac{\pi }{2}}{\int }_0^{\frac{\pi }{2}}{\int }_0^2{\rho }^{2}d\rho d\theta d\varphi }$

d) ${\displaystyle {\int }_0^{\frac{\pi }{4}}{\int }_0^{\frac{\pi }{4}}{\int }_0^{\cos \left(\varphi \right)}\cos \theta d\rho d\varphi d\theta }$

Find the indefinite integral.
$\int \frac{x^2-96}{x}dx$

$y^{\prime }-\sin 2x+y\tan x=0$

Explain why neither Substitution nor Integration by Parts would work to evaluate integral of ${\displaystyle \cos \left(x^2\right)dx}$

Prove using the definition on the limit that
${\displaystyle \underset{n\to \mathrm{\infty }}{lim}\frac{1+n}{1-2n}=\frac{-1}{2}}$

Evaluate the following
1.${\displaystyle \int e^x\sqrt{1-e^{2x}}dx}$
2. ${\displaystyle \int \frac{x^2}{\sqrt{5}+x^2}dx}$

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

Find the derivatives.
by evaluating the integral and differentiating the result.
${\displaystyle \frac{d}{d0}{\int }_0^{\tan 0}{\sec }^{2}ydy}$