No products in the cart.

Integration of 1/sinx+cosecx= ????

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Posted by Arpan Sahu 8 years, 3 months ago

Naveen Sharma 8 years, 3 months ago

Ans. $\int \frac{1}{\sin x + \cos e c x} d x$

=> $\int \frac{1}{\sin x + \frac{1}{\sin x}} d x$

=> $\int \frac{1}{\frac{\sin^{2} x + 1}{\sin x}} d x$

=> $\int \frac{\sin x}{1 + \sin^{2} x} d x$

=> $\int \frac{\sin x}{2 - \cos^{2} x} d x$

=> $\int \frac{- \sin x}{\cos^{2} x - 2} d x$

Put cos x = t then -sinx dx = dt

=> $\int \frac{1}{t^{2} - 2} d t$

=> $\int \frac{1}{t^{2} - {(\sqrt{2})}^{2}} d t$

We know that : $\int \frac{1}{x^{2} - a^{2}} d x = \frac{1}{2 a} \ln (\frac{(x - a)}{(x + a)}) + C$ , applying this on above. we get

=> $\frac{1}{2 \sqrt{2}} \ln (\frac{t - \sqrt{2}}{t + \sqrt{2}}) + C$

put value of t, we get

=> $\frac{1}{2 \sqrt{2}} \ln (\frac{\cos x - \sqrt{2}}{c o x s + \sqrt{2}}) + C$

ANSWER

Related Questions

What is the maximum value of sinx + cos x

Posted by Xxxxxx Xx 9 months, 2 weeks ago

CBSE > Class 12 > Mathematics

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Posted by Neemisha Gusain 10 months ago

CBSE > Class 12 > Mathematics

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Posted by Tumngam Karbak 10 months, 1 week ago

CBSE > Class 12 > Mathematics

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Posted by Suchitra Jain 9 months, 3 weeks ago

CBSE > Class 12 > Mathematics