integration of cosec x Integrate cosecx dx Solution Verified by Toppr I cscx dx I cscx cscx cotx cscx cotx dx Put cscx cotx t cscxcotx cscxx dx dt dx dt cscx cscx cotx I
What is Integration of Cosec X The most popular and commonly used integration of cosec x is ln cosecx cotx C However some other forms of the integral of cosec x are there They are as follows cosecx dx ln cosecx cotx C I cosecx dx 1 2 ln cosx 1 cosx 1 C I cosecx dx ln tanx 2 Integration of Cosecx or Cosec x The integration of cosec x is log cosec x cot x C or l o g t a n x 2 C where C is the integration constant i e cosec x log cosec x cot x C or cosec x l o g t a n x 2 C Proof Let I cosec x dx Multiply and divide both denominator and numerator by cosec x cot x
integration of cosec x
integration of cosec x
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Integration Of Cosec X
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Integral Of Cosec X Formula Proof Integration Of Cosec X
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Integral of the cosecant function denoted as cosec x dx signifies the enclosed area beneath the cosecant curve from a designated starting point to a particular endpoint along the x axis Mathematically it is typically represented as cosec x dx ln cosec x cot x C 1 Proof Strategy The strategy is not obvious Multiply and divide by csc x cot x use Substitution set u csc x cot x then we find du csc x cot x csc 2 x dx
int e x cos x dx int cos 3 x sin x dx int frac 2x 1 x 5 3 int 0 pi sin x dx int a b x 2dx int 0 2 pi cos 2 theta d theta partial fractions int 0 1 frac 32 x 2 64 dx substitution int frac e x e x e x dx u e x Show More To convert this integral to integrals of the form cosjxsinxdx rewrite sin3x sin2xsinx and make the substitution sin2x 1 cos2x Thus cos2xsin3xdx cos2x 1 cos2x sinxdx Let u cosx then du sinxdx u2 1 u2 du u4 u2 du 1 5u5 1 3u3 C 1 5cos5x 1 3cos3x C
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MATH HELP integration Of Cosecx YouTube
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Integration Of Cosecx YouTube
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Ex 7 9 8 Direct Integrate Cosec X Dx From Pi 6 To Pi 4
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Cosecx integration formula The integration formula of cosec x is given below cosecx dx ln cosecx cotx C where C is an integral constant Integration of Cosecx Proof We will prove that cosecx dx ln cosecx cotx C Note that cosecx dx cosecx 1 dx cosecx cosec x cot x cosec x cot x dx cosec 2 x cosec x cot Substitute u sin x text d u cos x d x to convert int sec 3 x d x into int frac d u 1 u 2 2 and evaluate the latter using the method of partial fractions This is done in Example 1 10 6 in Section
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What Is The Integral Of Csc x Epsilonify
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Cosec X Integration In Terms Of Tan X 2 How To Find It YouTube
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integration of cosec x - To convert this integral to integrals of the form cosjxsinxdx rewrite sin3x sin2xsinx and make the substitution sin2x 1 cos2x Thus cos2xsin3xdx cos2x 1 cos2x sinxdx Let u cosx then du sinxdx u2 1 u2 du u4 u2 du 1 5u5 1 3u3 C 1 5cos5x 1 3cos3x C