Calculus: Back again

Calculus Level pending

Assume f ( x ) f(x) is a linear function. For 0 < a < b 0<a<b the value of

∫ a b f ′ ′ ( x ) d x \large \int_a^b f''(x) ~ \mathrm{d}x

0 1 0 \dfrac{1}{0} a b ab b a \dfrac{b}{a} 1 a b \dfrac{a}{b}

Viki Zeta by Viki Zeta , 19, India

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1 solution

Anthony Holm
Nov 2, 2016

Any linear function is of the form f(x)=Ax+B, where A and B are constants. Then f'(x)=A and f''(x)=0. The integral of f''(x) from a to b is equal to f'(b)- f'(a)=A-A=0, by the fundamental theorem of calculus.

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