Find the Antiderivative -x^2

Problem

(∫_^)(−x2*d(x))

Solution

1. Identify the integral as a power function multiplied by a constant.

2. Apply the constant multiple rule by moving the negative sign outside the integral.

(∫_^)(−x2*d(x))=−(∫_^)(x2*d(x))

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

−(∫_^)(x2*d(x))=−((x(2+1))/(2+1))+C

4. Simplify the expression by performing the addition in the exponent and the denominator.

−((x3)/3)+C

5. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(−x2*d(x))=−(x3)/3+C

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