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CBSE Class 12 · 2009 · Definite IntegralsVery Short Answer

If

\int_{0}^{1} (3 x^{2} + 2 x + k) d x = 0

, find the value of

k

.

Answer: $k = - 2$

Solution

Integrate and apply the limits:

\int_{0}^{1} (3 x^{2} + 2 x + k) d x = [x^{3} + x^{2} + k x]_{0}^{1} = 1 + 1 + k = 2 + k

Setting this equal to

0

:

2 + k = 0 \Rightarrow k = - 2

.

CBSE Class 12 Board · 2009 · Subjective

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