what will be the integration of e to the power x sin square x dx?
what will be the integration of e to the power x sin square x dx?
Sumit Jha , 7 Years ago
Grade 12
Integral Calculus> what will be the integration of e to the ...
1 Answers
Arun
Let L = ∫ e^x*sin(2x) dx and use integration by parts.
Let:
u = sin(2x)
du = 2cos(2x) dx
dv = e^x dx
v = e^x
Then:
L = uv - ∫ v du
==> L = e^x*sin(2x) - 2 ∫ e^x*cos(2x) dx
Let:
u = cos(2x)
du = -2sin(2x)
dv = e^x dx
v = e^x
By another round of integration by parts:
L = e^x*sin(2x) - 2(uv - ∫ v du)
==> L = e^x*sin(2x) - 2[e^x*cos(2x) + 2 ∫ e^x*sin(2x) dx]
==> L = e^x*sin(2x) - 2e^x*cos(2x) - 4 ∫ e^x*sin(2x) dx
==> L = e^x*sin(2x) - 2e^x*cos(2x) - 4L (since L = ∫ e^x*sin(2x) dx)
==> 5L = e^x*sin(2x) - 2e^x*cos(2x)
==> 5L = e^x * [sin(2x) - 2cos(2x)]
==> L = e^x * [sin(2x) - 2cos(2x)]/5
==> ∫ e^x*sin(2x) dx = e^x * [sin(2x) - 2cos(2x)]/5 + C
Therefore, ∫ e^x*sin(2x) dx = e^x * [sin(2x) - 2cos(2x)]/5 +
Let:
u = sin(2x)
du = 2cos(2x) dx
dv = e^x dx
v = e^x
Then:
L = uv - ∫ v du
==> L = e^x*sin(2x) - 2 ∫ e^x*cos(2x) dx
Let:
u = cos(2x)
du = -2sin(2x)
dv = e^x dx
v = e^x
By another round of integration by parts:
L = e^x*sin(2x) - 2(uv - ∫ v du)
==> L = e^x*sin(2x) - 2[e^x*cos(2x) + 2 ∫ e^x*sin(2x) dx]
==> L = e^x*sin(2x) - 2e^x*cos(2x) - 4 ∫ e^x*sin(2x) dx
==> L = e^x*sin(2x) - 2e^x*cos(2x) - 4L (since L = ∫ e^x*sin(2x) dx)
==> 5L = e^x*sin(2x) - 2e^x*cos(2x)
==> 5L = e^x * [sin(2x) - 2cos(2x)]
==> L = e^x * [sin(2x) - 2cos(2x)]/5
==> ∫ e^x*sin(2x) dx = e^x * [sin(2x) - 2cos(2x)]/5 + C
Therefore, ∫ e^x*sin(2x) dx = e^x * [sin(2x) - 2cos(2x)]/5 +
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on integral calculus
The area of a square field is 640000cm2.what is its area in hectares
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available
Last Activity: 3 Years ago
Please solve this integration. I am facing difficulty in it How to solve this. Please solve anyone. Humble request
Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request
integral calculus
1 Answer Available
Last Activity: 3 Years ago
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
1 Answer Available
Last Activity: 3 Years ago
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
integral calculus
1 Answer Available
Last Activity: 4 Years ago