If 1 ∫ 0 ( 3 X 2 + 2 X + K ) D X = 0 , Find the Value of K. - Mathematics

Question

If \[\int\limits_0^1 \left( 3 x^2 + 2x + k \right) dx = 0,\] find the value of k.

Solution

\[\text{We have}, \]
\[ \int_0^1 \left( 3 x^2 + 2x + k \right) d x = 0\]
\[ \Rightarrow \left[ x^3 + x^2 + kx \right]_0^1 = 0\]
\[ \Rightarrow 1 + 1 + k - 0 = 0\]
\[ \Rightarrow k = - 2\]

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Definite Integrals

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Q 31 Q 30 Q 32

Chapter 20: Definite Integrals - Very Short Answers [Page 116]

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RD Sharma Mathematics [English] Class 12

Chapter 20 Definite Integrals
Very Short Answers | Q 31 | Page 116

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