Evaluate `int_(1)^(4)f(x)dx`, where `f(x)={{:(4x+3,"if" 1 le x le 2),(3x+5,"if" 2 le x le 4.):}`

Evaluate `int_(1)^(4)f(x)dx`, where `f(x)={{:(4x+3,"if" 1 le x le 2),(

1.	Evaluate `int_(1)^(4)f(x)dx`, where `f(x)={{:(4x+3,"if" 1 le x le 2),(3x+5,"if" 2 le x le 4.):}`
Answer» `int_(1)^(4)f(x)dx=int_(1)^(2)f(x)dx+int_(2)^(4)f(x)dx` `=int_(1)^(2)(4x+3)dx+int_(2)^(4)(3x+5)dx` `=[2x^(2)+3x]_(1)^(2)+[(3x^(2))/(2)+5x]_(2)^(4)=(9+28)=37`.

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The value of ` int _(0)^(pi//2) ((sin x + cos x)^(2))/(sqrt(1+sin 2x) dx` is
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If `int _(0)^(pi//2) sin^(6) dx = (5pi)/32 ,` then the value of ` int _(-pi)^(pi) (sin ^(6) x + cos^(6)x)dx` isA. `(5pi)/8`B. `(5pi)/16`C. `(5pi)/2`D. `(5pi)/4`
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`l=int_(-2)^(1)(tan^(-1)x+"cot"^(-1)(1)/(x))dx` is equal toA. ` (5pi)/2+ 4 tan ^(-1) 2 - In 5/2`B. ` (5pi)/2 - 4 tan^(-1) 2 + In 5/2`C. ` (5pi)/2 - 3 tan ^(-1) 2 - In 5/2`D. ` (5pi)/2 - 3 tan ^(-1) 2 + 5/2`
`int_0^pi(x dx)/(a^2cos^2x+b^2sin^2x)`A. `pi/(2ab)`B. `pi/(ab)`C. `(pi^(2))/(2ab)`D. `(pi^(2))/(ab)`