Mathematics

Solve:
$$\displaystyle \int_{0}^{T/2}{I_{0}\sin(wt)dt}$$


SOLUTION
$$\int_{0}^{T/2}I_{0} sin(wt).dt$$
$$=I_{0}\int_{0}^{T/2} sin (wt).dt$$
$$=I_{0}[\frac{-cos\,  wt}{w}]_{0}^{T/2}$$
$$= \frac{I_{0}}{w}[- cos\, w.\frac{T}{2}-(-cos 0)]$$
$$= \frac{I_{0}}{w}[-cos(\frac{2\pi }{T}.\frac{T}{2})+cos 0]$$
$$= \frac{I_{0}}{w}[- cos\pi + cos0]$$
$$= \frac{I_{0}}{w}[I+1]$$
$$= \frac{2I_{0}}{w}$$
$$= \frac{2I_{0}}{(\frac{2\pi }{T})}$$
$$= \frac{T.I_{0}}{\pi }$$

View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
$$\displaystyle \int { \frac { \cos { x } -\sin { x }  }{ \sqrt { 8-\sin { 2x }  }  } dx } $$ is equal to 
  • A. $$\sin ^{ -1 }{ \left( \sin { x } +\cos { x } \right) } +c$$
  • B. $$\cos ^{ -1 }{ \left( \sin { x } +\cos { x } \right) } +c$$
  • C. None of these
  • D. $$\displaystyle \sin ^{ -1 }{ \left[ \frac { 1 }{ 3 } \left( \sin { x } +\cos { x } \right) \right] } +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
If $$f(x)$$ is odd function and $$f(1)=a$$, and $$f(x+2)=f(x)+f(2)$$ then the value of $$f(3)$$ is 
  • A. $$6a$$
  • B. $$0$$
  • C. $$9a$$
  • D. $$3a$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
$$\dfrac { d y } { d x } = ( 4 x + y + 1 ) ^ { 2 }$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Find the integral of    $$\displaystyle \int \frac {x^3+3x+4}{\sqrt x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
$$\int\limits_0^\pi  {\dfrac{{x\sin x}}{{1 + {{\cos }^2}x}}dx} $$ equals:
  • A. $$0$$
  • B. $$\dfrac{\pi }{4}$$
  • C. $$\dfrac{\pi ^2}{2}$$
  • D. $$\dfrac{\pi ^2}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer