Problem

Find the antiderivative of the function f(x)=3x2−5x+7.

Answer

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Answer

Therefore, the antiderivative of f(x)=3x2−5x+7 is F(x)=x3−52x2+7x+C, where C is the constant of integration.

Steps

Step 1 ：The antiderivative of a function is found by reversing the process of differentiation. For the function f(x)=3x2−5x+7, we need to find a function F(x) such that F′(x)=f(x).

Step 2 ：The antiderivative of 3x2 is x3 because the derivative of x3 is 3x2.

Step 3 ：The antiderivative of −5x is −52x2 because the derivative of −52x2 is −5x.

Step 4 ：The antiderivative of 7 is 7x because the derivative of 7x is 7.

Step 5 ：Therefore, the antiderivative of f(x)=3x2−5x+7 is F(x)=x3−52x2+7x+C, where C is the constant of integration.

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