Question

if integrate (e^ax+bx)dx= e^4x/4+3x^2+c,then value of (a+b)=​

Answer 1

SOLUTION

GIVEN

$\displaystyle \int\limits_{}^{} ({e}^{ax} + bx)\, dx = \frac{ {e}^{4x} }{4} + \frac{3 {x}^{2} }{2} + c$

TO DETERMINE

The value of a + b

EVALUATION

Here it is given that

$\displaystyle \int\limits_{}^{} ({e}^{ax} + bx)\, dx = \frac{ {e}^{4x} }{4} + \frac{3 {x}^{2} }{2} + c$

$\displaystyle \int\limits_{}^{} {e}^{ax} \, dx + \displaystyle \int\limits_{}^{} bx\, dx = \frac{ {e}^{4x} }{4} + \frac{3 {x}^{2} }{2} + c$

On integration

$\displaystyle \frac{ {e}^{ax} }{a} + \frac{b {x}^{2} }{2} + c= \frac{ {e}^{4x} }{4} + \frac{3 {x}^{2} }{2} + c$

Comparing both sides we get

a = 4 and b = 3

∴ a + b = 4 + 3 = 7

FINAL ANSWER

The required value of a + b is 7

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