486(B)
The equation of a curve is y = f(x). The tangents at (1, f(1)), (2, f(2)) and (3, f(3)) make angles π6, π3 and π4 respectively with the positive direction of the x-axis. Then the value of 23∫f'(x).f"(x).dx +13∫f"(x).dx is equal to
(a) 1√3 (b) -1√3 (c) 0 (d) none of these.
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3 Answers
481f'(1)=1/√3
f'(2)=√3
f'(3)=1
Now separating the integration(I) into two parts-I1 and I2
I1=∫f'(x).f"(x).dx (with limits from 2 to 3)
I2=∫f"(x).dx (with limits from 1 to 3)
Now applying IBP in I1 we get the value as 1-3/2..i.e -1
And I2=f'(3)-f'(1)=1-1/√3
Now required integration(I)= I1+I2 =-1/√3
Hence B is correct......:)
- Anurag Ghosh In I1 (1-3)/2(forgot to mention dat) Upvote·0· Reply ·2013-08-06 07:05:52
865Limits are 2 to 3 and 1 to 3.
- Soumyadeep Basu This is actually quite easy.