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​ find a

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$$\int_1^a(3x^2-6x+3)dx=27$$

Guest Jun 6, 2018

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$$\text{Find } a: \int_1^a(3x^2-6x+3)dx=27$$

 After factoring the integrand: $$\int_1^a3(x-1)^2dx=(x-1)^3|_1^a=(a-1)^3=27$$ Taking the cube root: $$a-1=3 \Rightarrow a=\boxed4$$

$$\text{The solution you seek is } a=\boxed4\\$$

GYanggg  Jun 6, 2018
#1
+793
+2

$$\text{Find } a: \int_1^a(3x^2-6x+3)dx=27$$

 After factoring the integrand: $$\int_1^a3(x-1)^2dx=(x-1)^3|_1^a=(a-1)^3=27$$ Taking the cube root: $$a-1=3 \Rightarrow a=\boxed4$$

$$\text{The solution you seek is } a=\boxed4\\$$

GYanggg  Jun 6, 2018