Løs ∫ x^2 wrt x/sqrt{a^2-x^2} | Microsoft Problemløser til matematik

Evaluer

\frac{\sin(4\arcsin(\frac{x}{|a|}))a^{2}}{24}+\frac{\arcsin(\frac{x}{|a|})a^{2}}{2}-\frac{x^{5}}{3\sqrt{a^{2}-x^{2}}a^{2}}-\frac{2xa^{2}}{3\sqrt{a^{2}-x^{2}}}+\frac{x^{3}}{\sqrt{a^{2}-x^{2}}}+С

Differentier w.r.t. x

\frac{14\left(ax\right)^{2}+\cos(4\arcsin(\frac{x}{|a|}))a^{4}-8x^{4}-a^{4}}{6\sqrt{a^{2}-x^{2}}a^{2}}

Quiz

Integration

5 problemer svarende til:

\int \frac { x ^ { 2 } d x } { \sqrt { a ^ { 2 } - x ^ { 2 } } }

Lignende problemer fra websøgning

How to find the indefinite integral for \int \frac{x^2}{\sqrt{r^2 - x^2}}dx?

https://math.stackexchange.com/q/1663700

A good trick for choosing trigonometric substitutions is to draw a triangle. Here you want \sqrt{r^2-x^2} to be a trigonometric variable. That means the hypotenuse is r and one leg is x. Say ...

\displaystyle\int\frac{{{x}^{{2}}{\left.{d}{x}\right.}}}{{\sqrt{{{4}-{9}{x}^{{2}}}}}} ?

https://socratic.org/questions/int-x-2dx-sqrt-4-9x-2

\displaystyle\int\frac{{{x}^{{2}}{\left.{d}{x}\right.}}}{\sqrt{{{4}-{9}{x}^{{2}}}}}=\frac{{2}}{{27}}{\left({\arcsin{{\left(\frac{{3}}{{2}}{x}\right)}}}-\frac{{{3}{x}\sqrt{{{4}-{9}{x}^{{2}}}}}}{{4}}\right)}+{C} ...

Trig substitution for \int \frac{x^2dx}{\sqrt{4 - x^2}}

https://math.stackexchange.com/q/2631952

You've apparently used an incorrect trigonometric identity, \sin^2 t = \frac{1 + \sin 2t}{2}. This is correct only if you erase all the sines and write cosines instead; it is false if t = 0, ...

How do you integrate \displaystyle\int\frac{{{x}^{{2}}-{x}}}{\sqrt{{{9}-{x}^{{2}}}}}{\left.{d}{x}\right.} using trigonometric substitution?

https://socratic.org/questions/how-do-you-integrate-int-x-2-x-sqrt-9-x-2-dx-using-trigonometric-substitution

\displaystyle{I}=\frac{{9}}{{2}}{{\sin}^{{-{{1}}}}{\left(\frac{{x}}{{3}}\right)}}-\frac{{x}}{{2}}\sqrt{{{9}-{x}^{{2}}}}+\sqrt{{{9}-{x}^{{2}}}}+{c} Explanation: We know that, \displaystyle{\left({\left({1}\right)}{{\sin}^{{2}}{x}}=\frac{{{1}-{\cos{{2}}}{x}}}{{2}}\right)} ...

Find the exact value of \int_{0}^{a} \frac{dx}{x + \sqrt{a^{2} - x^{2}}}

https://math.stackexchange.com/questions/2152910/find-the-exact-value-of-int-0a-fracdxx-sqrta2-x2

A standard substitution would be x=a\sin t, so dx=a\cos t\,dt and \sqrt{a^2-x^2}=a\cos t (assuming a>0). The integral thus becomes I=\int_0^{\pi/2}\frac{\cos t}{\sin t+\cos t}\,dt which ...

Evaluation of the integrals \int_{0}^{a}\frac{dx}{\sqrt{ax-x^2}} and \int\frac{3x^5dx}{1+x^{12}}

https://math.stackexchange.com/questions/463814/evaluation-of-the-integrals-int-0a-fracdx-sqrtax-x2-and-int-f

HINT: For \int_0^a\frac{dx}{\sqrt{ax-x^2}}=\int_0^a\frac{dx}{\sqrt{x(a-x)}}=\int_0^a\frac{dx}{|a|\sqrt{\frac xa(1-\frac xa)}} Putting x=a\sin^2y,dx=2a\sin y\cos y dy and as x=0\implies y=0;x=a\implies y=\frac\pi2 ...

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Eksempler

Kvadratisk ligning

{ x } ^ { 2 } - 4 x - 5 = 0

Trigonometri

4 \sin \theta \cos \theta = 2 \sin \theta

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]

Samtidig ligning

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

Differentiering

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

Grænser

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

Emner

Emner

Lignende problemer fra websøgning

Aktie

Eksempler