Question

$\int\limits^a_0 {(2x+1)} \, dx=2$; Find the real value of 'a'.

Answer 1

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Answer 2

Answer:

a = -2

a = 1

Step-by-step explanation:

$\limits^a__0\int\:(2x+1)\:dx = 2$

to find the value of a,first integrate the function and put limits than we can find the value of a

$\int\:2x\:dx+\int\:1\:dx\\\\=\frac{2x^{2} }{2}+x+C\\\\=x^{2}+x$

now put the values

$[x^{2}+x]\limits^a___0 \,$

$a^{2}+a=2\\ \\ a^{2}+a-2 =0\\ \\a^{2}+2a-a-2=0\\ \\ a(a+2)-1(a+2)=0\\ \\(a+2)(a-1)=0\\ \\a=-2\\ \\ a=1$