CUET · MATHS · PYQ PAPER 2023
If \(\int_0^1\left(3 x^2+2 x+5 k\right) d x=0\), then the value of \(k\) is:
- A \(\frac{3}{5}\)
- B \(-\frac{2}{5}\)
- C \(\frac{2}{5}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(B) \(-\frac{2}{5}\)
Step-by-step Solution
Detailed explanation
\(\int_0^1(3x^2+2x+5k)dx=0\) \(\left[x^3+x^2+5kx\right]_0^1=0\) \((1^3+1^2+5k(1))-(0)=0\) \(1+1+5k=0\) \(2+5k=0\) \(5k=-2\) \(k=-\frac{2}{5}\)
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