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AP EAMCET · Maths · Indefinite Integration

Suppose that \(f\) and \(g\) are integrable on \([a, b]\), then \(f+g\) is integrable on ......... .

  1. A \((a, b)\)
  2. B Cannot comment
  3. C \([a, b]\)
  4. D Range of \(f+g\)
Verified Solution

Answer & Solution

Correct Answer

(C) \([a, b]\)

Step-by-step Solution

Detailed explanation

As \(f\) and \(g\) are integrable on \([a, b]\), then \(\int_{x_1}^{x_2} f(x) d x\) and \(\int_{x_1}^{x_2} g(x) d x\) exists for every value of \(x_1, x_2 \in[a, b]\), then \(\int_{x_1}^{x_2} f(x) d x+\int_{x_1}^{x_2} g(x) d x=\int_{x_1}^{x_2}(f+g)(x) d x\) Also exists for…