JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023Choose the correct answer:
- A.
loge(1+5(2+5)2)+25
loge(1+52(2+5)2)−25
Explanation
Step 1: Substitution
Maana t=ex, toh dt=exdx.
Ab limits badalte hain:
-
Lower limit: Jab x=−loge2⟹t=eloge2−1=21
-
Upper limit: Jab x=loge2⟹t=2
Ab integral ye ban jayega:
Step 2: Integration by Parts
Hum ∫u⋅vdt ka formula lagayenge, jahan u=loge(t+1+t2) aur v=1 hai.
Hame pata hai ki dtd[loge(t+1+t2)]=1+t21.
Step 3: Limits aur Integration apply karna
Pehle part mein limits rakhne par:
Doosre part ka integral:
Limits lagane par:
Step 4: Final Simplification
Sabko ek saath likhne par:
Explanation
Step 1: Substitution
Maana t=ex, toh dt=exdx.
Ab limits badalte hain:
-
Lower limit: Jab x=−loge2⟹t=eloge2−1=21
-
Upper limit: Jab x=loge2⟹t=2
Ab integral ye ban jayega:
Step 2: Integration by Parts
Hum ∫u⋅vdt ka formula lagayenge, jahan u=loge(t+1+t2) aur v=1 hai.
Hame pata hai ki dtd[loge(t+1+t2)]=1+t21.
Step 3: Limits aur Integration apply karna
Pehle part mein limits rakhne par:
Doosre part ka integral:
Limits lagane par:
Step 4: Final Simplification
Sabko ek saath likhne par:

