Evaluate the integral.
-$$\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 3 } d x$$

Question

Quizplus · Accepted Answer

To solve the integral $\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 3 } d x$, we first find the antiderivative of the integrand. The antiderivative of $(x + 1)^3$ is $\frac{1}{4}(x + 1)^4$. Applying the Fundamental Theorem of Calculus, we evaluate this antiderivative from 0 to 1: $$\left. \frac{1}{4}(x + 1)^4 \right|_0^1 = \frac{1}{4}(2^4) - \frac{1}{4}(1^4) = \frac{16}{4} - \frac{1}{4} = 4 - \frac{1}{4} = \frac{15}{4}.$$

Evaluate the Integral ∫01(x+1)3dx\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 3 } d x∫01​(x+1)3dx

Evaluate the Integral $\int _ { 0 } ^ { 1 } ( x + 1 ) ^ { 3 } d x$