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If $f (x) = x | x |$ , then for any real number $a$ and $b$
with $a < b,$ the value of $\int_{a}^{b} f (x) d x$ equals

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detailed solution

Correct option is A

∫ab f(x)dx=∫ab x|x|dx=∫ab −x2dxb<0∫a0 −x2dx+∫0b x2dx,a<0

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If f(x)=x|x| , then for any real number a and b with a<b, the value of ∫ab f(x)dx equals

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $f (x) = x | x |$ , then for any real number $a$ and $b$
with $a < b,$ the value of $\int_{a}^{b} f (x) d x$ equals