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Vor 3 Tagen · Definition: Definite Integral. If f(x) is a function defined on an interval [a, b], the definite integral of f from a to b is given by. ∫b af(x)dx = lim n → ∞ n ∑ i = 1f(x ∗ i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a, b], or is an integrable function.
Vor 17 Stunden · I evaluate the integral of 2x^2(x^3-5)^6 dx using substitution. If this content is helpful, please subscribe.
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Vor einem Tag · Integration of x^2 e^x dx | Integration | #algebra #integration #jee #maths@eyei88 #jee #integral #integration #algebra
- 11 Sek.
- eYei
Vor 4 Tagen · Wie berechne ich das Integral \( \int\limits_{b}^{\infty} \)1/(Wurzel(2π)*o)*x*\( e^{-\frac{(x-u)²}{o²}} \) ? Die Integralrechner zeigen mir Lösungen mit der Funktion erfi an die wir aber noch nicht hatten. Ich habe versucht das Integral mit partieller Integration zu lösen aber es kommt am Ende nichts richtiges raus unser Prof meinte aber ...
Vor 3 Tagen · I used the substitution $\sqrt{1+\sin(y)} \rightarrow x$. This transforms the integral into: $$-2\int_{1}^{\sqrt{2}}\frac{\ln(x^{2}-1)}{x^{2}-2}dx.$$ I further decomposed the logarithm: $$-2\int_{1}^{\sqrt{2}}\frac{\ln(x+1)+\ln(x-1)}{(x-\sqrt{2})(x+\sqrt{2})}dx.$$ I'm stuck at this point.
Vor 3 Tagen · $$\int^{π/2}_0 \frac{\cos^2(x)}{\cos^2(x)+4\sin^2(x)}dx$$ We can multiply the numerator and denominator by $\sec^4(x)$ and get $$\int^{π/2}_0 \frac{\sec^2(x)}{\sec^2(x)+4\sec^2(x)\tan^2(x)}dx$$
This is solvable by hand with two steps of integration by parts. If you actually want to see what Mathematica is doing under the hood with Integrate[(Log[x]/x)^2,x] you can use Trace with TraceInternal set to True : Note that the methods of Integrate aren't really designed to be human-readable, and can be quite confusing so they require a lot ...
