Tip:A–D to answerE for explanationV for videoS to reveal answer
If [t] denotes the greatest integer ≤t, then the value of e3(e−1)∫12x2e[x]+[x3]dx is:
- A.
e8−1
- B.
e7−1
- C.
e8−e
(Correct Answer) - D.
Explanation
Solution:
-
Interval x∈[1,2) mein [x]=1:
I=e3(e−1)∫12x2e1+[x3]dx=3(e−1)∫12x2e[x3]dx
-
Substitution: Let x3=t⟹3x2dx=dt. Jab x=1,t=1 aur jab x=2,t=8.
-
Integral ko todna:
I=(e−1)[e1+e2+e3+e4+e5+e6+e7]
Explanation
Solution:
-
Interval x∈[1,2) mein [x]=1:
I=e3(e−1)∫12x2e1+[x3]dx=3(e−1)∫12x2e[x3]dx
-
Substitution: Let x3=t⟹3x2dx=dt. Jab x=1,t=1 aur jab x=2,t=8.
-
Integral ko todna:
I=(e−1)[e1+e2+e3+e4+e5+e6+e7]
