Question
If f(x)=√x,g(x)=ex−1,and∫fog(x)dx=Afog(x)+Btan−1(fog(x))+C, then A + B is equal to
Answer: Option D
:
D
fog(x)=√ex−1∴I=∫√ex−1dx=∫2t2t2+1dt{wheret=√ex−1}=2t−2tan−1t+C=2√ex−1−2tan−1(√ex−1)+C=2fog(x)−2tan−1(fog(x))+C∴A+B=2+(−2)=0
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:
D
fog(x)=√ex−1∴I=∫√ex−1dx=∫2t2t2+1dt{wheret=√ex−1}=2t−2tan−1t+C=2√ex−1−2tan−1(√ex−1)+C=2fog(x)−2tan−1(fog(x))+C∴A+B=2+(−2)=0
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