AP EAMCET · Maths · Definite Integration
Consider the following statements (A) and (B)
(A) \(\int_a^b \frac{d}{d x}(f(x)) d x=\frac{d}{d x} \int_a^b(f(x)) d x\)
(B) \(\frac{d}{d x}\left(\int f(x) d x\right)=f(x)+C\)
Which one of the following is true?
- A Only (A) is true
- B Only (B) is true
- C Both \((\mathrm{A})\) and \((\mathrm{B})\) are true
- D Both (A) and (B) are false
Answer & Solution
Correct Answer
(D) Both (A) and (B) are false
Step-by-step Solution
Detailed explanation
\(\int_a^b \frac{d}{d x}(f(x)) d x=\int_a^b d(f(x))=f(b)-f(a)\) ...(i) and \(\frac{d}{d x} \int_a^b f(x) d x=\frac{d}{d x}[\mathrm{~A}\) constant \(]=0\) ...(ii) \(\left\{\because \int_a^b f(x) d x\right.\) will necessarily give a constant value Hence…
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