Relating to integrations consisting of only(mainly) trigonometric functions and/or requiring substitutions by/of trigonometric functions.
Questions tagged [trigonometric-integrals]
1457 questions
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why the ending symbol dx is also changed into a function of d theta and then multiplied by the integral after substitution?
This is a question about trig substitution used in integrals.
Because it is difficult to solve an integral when there is radical in it, we use a trig function of theta to substitute x from the original integral.
The only thing I don't understand is…
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How to prove $\int_{-\pi}^{\pi}\cos(m(x-y))\cos(n(x-y))dx=\pi\delta_{mn}(2-H_1(m))$
I have encountered such a integral formula that I cannot prove.
$$\int_{-\pi}^{\pi}\cos(m(x-y))\cos(n(x-y))dx=\pi\delta_{mn}(2-H_1(m))$$
where $H_1(m)=\begin{cases}
0 & \text{if } m=0\\
1 & \text{if } m\geq1
\end{cases}$
If being converted to the…
MathArt
- 1,053
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2 answers
Intution for integral of sine function
Taking the above plot I'm looking for some intuition how to think about the integral of $sin(x)$, which is $-cos(x)$ (plus some constant that's assumed to be zero for the sake of readbility). The derivative of $sin(x)$ is easily interpreted…
Michael H
- 103
- 2
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Trigonometric Substiution
I am currently working on a practice problem on trig substitution.
I have no problem solving it my way but I don’t see how i can use the below stated identity and partial integration.
(I am sorry i am not using mathjax, im looking into it but it is…
Ang
- 415
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Where did I go wrong with this Integral?
My integral is $$\int \frac{dx}{x \sqrt{3-x^2}}$$
so I used trig substitution,
let $x$ = $\sqrt{3}\cos{\theta}$
let $dx$ = $-\sqrt{3}\sin{\theta}\ d\theta$
$$\int \frac{-\sqrt{3}\sin{\theta}\…
Ryan
- 1,200
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How do I solve $\int \frac{\sqrt {x^2+16}}{x^4}dx$ using trig substitution?
I have a problem requiring trigonometric substitution to evaluate $\int \frac{\sqrt {x^2+16}}{x^4}dx$.
This is how far I have gotten:
Let $ x = 4\tan \theta $
Then $dx = 4\sec^2\theta$
$$\int \frac{\sqrt…
Isaiah Banta
- 57
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2 answers
How do I solve this trigonometric substitution integral?
I know for a fact that it's a trig substitution where u=tanØ (let's pretend Ø is theta) and u=x and a=1.
For some reason, I keep going in circles.
This is the integral that I need to solve
Phia
- 29
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2 answers
how do i rewrite as a algebraic expression
please rewrite this trigonometric expression $\cos(\tan^{-1}(u)+\sin^{-1}(v))$ as an algebraic expression? I tried the sum differences method and could get no further
rwils157
- 1