© examsiri.com
Question : 76 of 150
Marks:
+1,
-0
Solution:
‌ Put ‌x‌=tan‌θ⇒dx= sec2θdθ∴‌‌f(x)‌=∫‌| tan2θ sec2θdθ |
| sec2θ(1+ secθ) |
‌=∫‌‌=∫‌| sin‌2θdθ |
| cos‌θ(1+cos‌θ) |
‌=∫‌| 1−cos2θdθ |
| cos‌θ(1+cos‌θ) |
‌=∫‌| (1−cos‌θ)dθ |
| cos‌θ |
‌=∫ secθdθ−∫dθ‌=log| secθ+tan‌θ|−θ+c ‌∴‌‌f(x)=log‌|x+√1+x2|−tan−1x+c‌∴f(0)=log|0+√1+0|−tan−1(0)+c‌⇒‌‌0=log‌1−0+c⇒c=0‌∴f(x)=log‌|x+√1+x2|−tan−1x‌∴f(1)=log‌|1+√1+12|−tan−1(1)‌=log(1+√2)−‌‌
© examsiri.com
Go to Question: