If $\int_{0}^{1}\left(5 x^{2}-3 x+k\right) d x=0$, then $k=$

If $\int_{0}^{1}\left(5 x^{2}-3 x+k\right) d x=0$, then $k=$
  1. $\frac{1}{3}$
  2. $\frac{1}{6}$
  3. $\frac{-1}{3}$
  4. $\frac{-1}{6}$

Solution

Given $\int_{0}^{1}\left(5 x^{2}-3 x+k\right) d x=0$ $\therefore\left[5 \frac{x^{3}}{3}-\frac{3 x^{2}}{2}+k x\right]_{0}^{1}=0 \Rightarrow \frac{5}{3}-\frac{3}{2}+k=0 \Rightarrow k=-\frac{1}{6}$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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