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if f ‘(x) = a sin x + b cos x and f ‘(0) = 4 , f(0) = 3 , f(pi/2) =5 find f(x)

if f ‘(x) = a sin x + b cos x and f ‘(0) = 4 , f(0) = 3 , f(pi/2) =5 find f(x)

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

f'(x) = asinx+bcosx
f'(0) = asin(0)+bcos(0)
4 = b
f'(x) = asinx+4cosx
\frac{df(x)}{dx} = asinx+4cosx
df(x) = (asinx+4cosx)dx
\int df(x) = \int (asinx+4cosx)dx
f(x) = -acosx+4sinx+c
f(0) = -acos(0)+4sin(0)+c
3 = -a+c.........(1)
f(\pi /2) = -acos(\pi /2)+4sin(\pi /2)+c
5 = 4+c
c=1
a = -2
f(x) = 2cosx+4sinx+1



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