antiderivative of sinx Let s start off with what we know intcosxdx sinx because the derivative of sinx is cosx We just have to adjust for that pesky 2 Let s think for a moment intcos2xdx essentially means that if we take the derivative of our solution we should get cos2x Let s guess a solution of 1 2sin2x and see what happens when we differentiate it
Use integration by parts udv uv vdu So for exsin x dx We should let u sin x du cos x dx dv exdx dv exdx v ex Plugging these into the integration by parts formula we see that exsin x dx exsin x excos x dx Explanation 1 sinx cscx cscx cscx cotx cscx cotx The numerator is the opposite the negative of the derivative of the denomoinator So the antiderivative is minus the natural logarithm of the denominator ln abs cscx cot x If you ve learned the technique of substitution we can use u cscx cot x so du csc 2 x cscx cotx
antiderivative of sinx
antiderivative of sinx
https://useruploads.socratic.org/QuiY16ySS2HAoSAVnZVI_Int2_1.jpg
How Do You Find The Antiderivative Of Int Sin 2xdx Socratic
https://useruploads.socratic.org/Z3QUHA2SDLrPYGscmEtA_integral.jpeg
4 8 2 Some Trigonometric Antiderivatives YouTube
https://i.ytimg.com/vi/I9_i8vv1ucQ/maxresdefault.jpg
Choose your u to be x so that way du dx 1 du dx That means dv sinxdx dv sinxdx v cosx The integration by parts formula is udv uv vdu We have u x du dx and v cosx Substituting into the formula gives xsinxdx xcosx cosx dx XX xcosx cosxdx XX xcosx What is the antiderivative of 1 sinx 1 sinx Calculus Introduction to Integration Integrals of
Remark If you write down a medium ugly elementary function like frac e x x 2 1 or even sqrt 1 x x 5 the function will usually not have an elementary antiderivative this makes for real trouble when we are trying to invent new arclength problems I just blogged another solution to this question in my blog The idea is to consider the following function G x x2cos1 x if x 0 0 if x 0 which is differentiable Clearly G x sin1 x 2xcos1 x if x 0 0 if x 0 Hence G f h where h x 2xcos1 x if x 0 0 if x 0
More picture related to antiderivative of sinx
How Do You Integrate sinx 2 Dx Socratic
https://useruploads.socratic.org/hUsCWV2TS2zF0fAQwPl0_Int1_1.jpg
What Is The antiderivative Of Sinx YouTube
https://i.ytimg.com/vi/RT0NJVrvWt0/maxresdefault.jpg
Find The Integral Of Sinx Sin x A YouTube
https://i.ytimg.com/vi/6IT-3V0xeQA/maxresdefault.jpg
If you mean sinx 3 please see below If you mean sin x 3 I can t help Here is one possibility int sinx 3 dx int sin 2x sinx dx int 1 cos 2 x sinx dx int sinx dx int underbrace cos 2x u underbrace sinx dx du cosx cos 3x 3 C As is typical of expressions involving trigonometric functions there are other ways to express this family of This is a part of the Fundamental Theorem of Calculus FTC The FTC bidirectionally relates differentiation and integration The first part tells you that antidifferentiation can be used to find an integral in particular if you have a function f with antiderivative F D 1 f then b af x dx F b F a The second part tells you
[desc-10] [desc-11]
Video 2034 23 Integrate Sinx Ln sinx YouTube
https://i.ytimg.com/vi/au1nfG2ELAM/maxresdefault.jpg
Antiderivative Of Sinx By Yatendra Parashar Issuu
https://image.isu.pub/120510094921-cb8bbc91dcbf44c8ab47375ca492a2b0/jpg/page_1.jpg
antiderivative of sinx - [desc-14]