Question

Analise o seguinte problema de integral

Answer 1

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$\displaystyle\sf\int[cos(2x)+2sen(x)]dx\\\boxed{\boxed{\boxed{\displaystyle\sf\int cos (a t)~dt=\dfrac{1}{a}sen(at)+k}}}\\\boxed{\boxed{\boxed{\displaystyle\sf\int sen(at)~dt=-\dfrac{1}{a}cos(at)+k}}}\\\displaystyle\sf\int[cos(2x)+2sen(x)]~dx=\int cos(2x)~dx+2\int sen(x)~dx\\\sf =\dfrac{1}{2}sen(2x)-2cos(x)+k\\\sf j(x)=\dfrac{1}{2}sen(2x)-2cos(x)+k\\\sf J(1)=\dfrac{1}{2}sen(2\cdot1)-2cos(1)+k\\\sf\dfrac{0,90}{2}-2\cdot0,54+k=2\cdot2\\\sf 0,90-4\cdot0,54+2k=4\\\sf 2k=4+4\cdot0,54-0,90\\\sf 2k=5,26$

$\sf k=\dfrac{5,26}{2}\\\sf k=2,63\\\sf J(x)=\dfrac{1}{2}sen(2x)-2cos(x)+2,63\\\sf J(5)=\dfrac{1}{2}sen(2\cdot5)-2\cdot cos(5)+2,63\\\huge\boxed{\boxed{\boxed{\boxed{\sf J(5)=1,79\checkmark}}}}$