MHT CET · Maths · Definite Integration
If \(\int_{0}^{1}\left(5 x^{2}-3 x+k\right) d x=0\), then \(k=\)
- A \(\frac{1}{3}\)
- B \(\frac{1}{6}\)
- C \(\frac{-1}{3}\)
- D \(\frac{-1}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{-1}{6}\)
Step-by-step Solution
Detailed explanation
Given \(\int_{0}^{1}\left(5 x^{2}-3 x+k\right) d x=0\)
\(\therefore\left[5 \frac{x^{3}}{3}-\frac{3 x^{2}}{2}+k x\right]_{0}^{1}=0 \Rightarrow \frac{5}{3}-\frac{3}{2}+k=0 \Rightarrow k=-\frac{1}{6}\)
\(\therefore\left[5 \frac{x^{3}}{3}-\frac{3 x^{2}}{2}+k x\right]_{0}^{1}=0 \Rightarrow \frac{5}{3}-\frac{3}{2}+k=0 \Rightarrow k=-\frac{1}{6}\)
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