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Integrate the following functions 1/sqrt(8+3x-x^2) |
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Answer» Solution :`8+3x-X^2 = 8-(x^2-3x)` `=8-(x^2-3x+9/4-9/4)` =`(41)/4 -(x_3/2)^2` THEREFORE `int 1/SQRT(8+3x-x^2)DX` =`int 1/sqrt((41)/4-(x-3/2)^2 dx` =`sin^-1(x-(3/2)/(sqrt41)/2)+c` =`sin^-1((2x-3)/sqrt(41))+c` |
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