Find the Antiderivative f(x)=144-x^2

Problem

(∫_^)(144−x2*d(x))

Solution

1. Identify the integral as a sum of two separate terms using the linearity property of integration.

(∫_^)(144−x2*d(x))=(∫_^)(144*d(x))−(∫_^)(x2*d(x))

2. Apply the constant rule to the first term, where the integral of a constant k is k*x

(∫_^)(144*d(x))=144*x

3. Apply the power rule to the second term, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1) for n≠−1

(∫_^)(x2*d(x))=(x3)/3

4. Combine the results and add the constant of integration C

144*x−(x3)/3+C

Final Answer

(∫_^)(144−x2*d(x))=144*x−(x3)/3+C

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