If f is continuously differentiable function then ∫$$02.5$$ $$x2f$$′$$(x)dx$$ is equal to

Question

If f is continuously differentiable function then ∫$$02.5$$ $$x2f$$′$$(x)dx$$ is equal to

Infinity Learn · Accepted Answer

∫$$02.5$$ $$x2f$$′(x)dx=$$∫$$01$$ $$x2f$$′$$(x)dx+$$∫$$12$$ $$x2f$$′$$(x)+$$∫$$23$$ $$x2f$$′$$(x)dx+$$∫$$32$$ $$x2f$$′$$(x)dx+$$∫$$25$$ $$x2f$$′$$(x)dx+$$∫$$56$$ $$x2f$$′$$(x)dx+$$∫$$625$$ $$x2f$$′$$(x)dx=0+$$∫$$12$$ f′$$(x)dx+2$$∫$$23$$ f′$$(x)dx+3$$∫$$32$$ f′$$(x)dx+4$$∫$$25$$ f′$$(x)dx+5$$∫$$56$$ f′$$(x)dx+6$$∫$$62.5$$ f′$$(x)dx=(f(2)−$$f(1))+2(f(3)$$−$$f(2))+3(f(2)$$−$$f(3))+4(f(5)$$−$$f(2))+5$$[$$f(6)$$−$$f(5)$$]$$+6$$[$$f(2.5)$$−$$f(6)$$]$$=6f(2.5)$$−(f(1)+f(2)+f(3)+f(2)+(f(5)+f(6))

If $f$ is continuously differentiable function then
$\int_{0}^{2.5} [x^{2}] f^{'} (x) d x$ is equal to

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If f is continuously differentiable function then ∫02.5 x2f′(x)dx is equal to

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If $f$ is continuously differentiable function then
$\int_{0}^{2.5} [x^{2}] f^{'} (x) d x$ is equal to