Risolvi f ( x ) = ∫ (from 2 to x) of (1/2t^2-1)^6dt | Microsoft Math Solver

Calcola

\int_{2}^{x} \frac{( t ^{2} - 2 ) ^{6}}{6 4} d t

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Differenzia rispetto a x

\frac{( x ^{2} - 2 ) ^{6}}{6 4}

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5 problemi simili a:

f (x) = \int_{2}^{x} (\frac{1}{2} t^{2} - 1)^{6} d t

Problemi simili da ricerca Web

Evaluating the integral

\int \frac{x ^{2} - 2 x - 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )}

https://math.stackexchange.com/questions/1632009/evaluating-the-integral-int-fracx2-2x-1x-12x21/1632024

Notice: Your way of using partial fractions is right, and it works in general. Use this to find the partial fractions. The integral of

\frac{1}{x}

ln ∣ x ∣ + C

i

Banach Contraction mapping of

Φ (f) (x) = \int_{0}^{x} \frac{1}{1 + f ( t ) ^{2}} d t

, find a fixed point.

https://math.stackexchange.com/questions/1778310/banach-contraction-mapping-of-phifx-int-0x-frac11ft2dt-find

A useful approach for these sorts of estimates is to use the mean value theorem. (a) Let

g (x) = \frac{1}{1 + x ^{2}}

g^{'} (x) = - \frac{2 x}{( 1 + x ^{2} ) ^{2}}

g^{''} (x) = 2 \frac{3 x ^{2} - 1}{( 1 + x ^{2} ) ^{3}}

\int_{S} x^{2} d σ = \frac{a ^{4} π}{4}

S

is a disk of radius

a

centered at the origin in the plane

z = 0

https://math.stackexchange.com/questions/2314154/show-that-int-sx2-d-sigma-fraca4-pi4-where-s-is-a-disk-of-rad

With polar coordinates, the first integral becomes

\int_{0}^{a} \int_{0}^{2 π} (r cos (t))^{2} (r) d r d t

= \int_{0}^{a} r^{3} d r \int_{0}^{2 π} cos^{2} (t) d t

= \frac{a ^{4}}{4} [\frac{t}{2} + \frac{1}{4} sin (2 t)]_{0}^{2 π}

f

be a continuous function and

f (x) = \frac{2}{t ^{2}} \int_{0}^{t} f (x + s) s d s

\forall t > 0 .

f

https://math.stackexchange.com/q/2471603

While your point is taken, I think some rephrasing will do this the world of good. Fix

x

h (t) = \frac{2}{t ^{2}} \int_{0}^{t} f (x + s) s d s

. By definition, we know that

h (t)

is a constant, for all ...

Fundamental Theorem and Integral Problem

https://math.stackexchange.com/questions/576419/fundamental-theorem-and-integral-problem

You are on the correct path. You applied the fundamental theorem of calculus correctly and deduced (almost) correctly that

F^{'} (x) = \frac{9 x ^{8}}{5 + ( x ^{9} ) ^{2}} = \frac{9 x ^{8}}{5 + x ^{18}} .

All you have to ...

Prove second derivative of

g

is proportional to

g^{2}

https://math.stackexchange.com/questions/912691/prove-second-derivative-of-g-is-proportional-to-g2

\begin{align} y & = \int_0^x (1+t^3)^{-1/2} \, dt, \\[10pt] \frac{dy}{dx} & = (1+x^3)^{-1/2}, \\[10pt] \frac{dx}{dy} & = \frac{1}{(1+x^3)^{-1/2}} = (1+x^3)^{1/2} = \text{some function of }y. \\[10pt] ...

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Esempi

Equazione quadratica

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

4 sin θ cos θ = 2 sin θ

Equazione lineare

y = 3 x + 4

699 * 533

[2534] [2 - 1 0135]

Equazione simultanea

{8 x + 2 y = 46 7 x + 3 y = 47

Differenziazione

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

\int_{0}^{1} x e^{- x^{2}} d x

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