Grade 12Integral Calculus

∫ xe^x cosx dx= f(x)+c, then find f(x).

PIYUSH AGRAWAL

15 Years agoGrade 12

Rathod Shankar AskiitiansExpert-IITB

15 Years ago

integral by parts take x and e^x cosx as two parts

$\int f g\, dx = f \int g\, dx - \int \left ( f' \int g\,dx \right )\, dx.\!$

take f=x and g=e^x cosx

here iam giving method for integration for e^x cosx ...i think u can solve now right. do practice so that u can get more concept

$\int e^{x} \cos (x) \, dx\!$

$u = \cos(x) \Rightarrow du = -\sin(x)\,dx$

$dv = e^x \, dx \Rightarrow v = \int e^x \, dx = e^x$

$\int e^{x} \cos (x) \, dx = e^{x} \cos (x) + \int e^{x} \sin (x) \, dx.\!$

$u = \sin(x) \Rightarrow du = \cos(x)\, dx$

$dv = e^x \, dx \Rightarrow v = \int e^x \, dx = e^x$

$\int e^x \sin (x) \, dx = e^x \sin (x) - \int e^x \cos (x) \,dx$

Putting these together,

$\int e^x \cos (x) \,dx = e^x \cos (x) + e^x \sin (x) - \int e^x \cos (x) \, dx.$

$2 \int e^{x} \cos (x) \, dx = e^{x} ( \sin (x) + \cos (x) ) + C\!$

$\int e^x \cos (x) \,dx = {e^x ( \sin (x) + \cos (x) ) \over 2} + C'\!$

Now you can win exciting gifts by answering the questions on
Discussion Forum. So help discuss any query on askiitians forum and
become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the
Askiitians Toolbar : Click here to download the toolbar..

∫ xe^x cosx dx= f(x)+c, then find f(x).

PIYUSH AGRAWAL

1 Answer

Rathod Shankar AskiitiansExpert-IITB

The area of a square field is 640000cm².what is its area in hectares

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

If 4th term of an A.p is zero, show that the 8th term is double the 6th term

∫ xex cosx dx= f(x)+c, then find f(x).

PIYUSH AGRAWAL

1 Answer

Rathod Shankar AskiitiansExpert-IITB

Other Related Questions on integral calculus

The area of a square field is 640000cm2.what is its area in hectares

Please solve this integration. I am facing difficulty in it How to solve this. Please solve anyone. Humble request

Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0

If 4th term of an A.p is zero, show that the 8th term is double the 6th term

∫ xe^x cosx dx= f(x)+c, then find f(x).

The area of a square field is 640000cm².what is its area in hectares

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0