91Ó°ÊÓ

Evaluate the definite integral. $$ \int_{0}^{1} x^{2} d x $$

Let $$ \begin{array}{l} \text { - } \int_{0}^{3} s(t) d t=10 \\ \text { - } \int_{3}^{5} s(t) d t=8 \\ \text { - } \int_{3}^{5} r(t) d t=-1, \text { and } \\ \text { - } \int_{0}^{5} r(t) d t=11 \end{array} $$ Use these values to evaluate the given definite integrals. $$ \int_{0}^{3}(s(t)+r(t)) d t $$

Find \(n\) such that the error in approximating the given definite integral is less than 0.0001 when using: (a) the Trapezoidal Rule (b) Simpson's Rule $$ \int_{0}^{\pi} \cos \left(x^{2}\right) d x $$

Evaluate the given indefinite integral. $$ \int(2 t+3)^{2} d t $$

Evaluate the definite integral. $$ \int_{0}^{1} x^{3} d x $$

Find \(n\) such that the error in approximating the given definite integral is less than 0.0001 when using: (a) the Trapezoidal Rule (b) Simpson's Rule $$ \int_{0}^{5} x^{4} d x $$

Let $$ \begin{array}{l} \text { - } \int_{0}^{3} s(t) d t=10 \\ \text { - } \int_{3}^{5} s(t) d t=8 \\ \text { - } \int_{3}^{5} r(t) d t=-1, \text { and } \\ \text { - } \int_{0}^{5} r(t) d t=11 \end{array} $$ Use these values to evaluate the given definite integrals. $$ \int_{5}^{0}(s(t)-r(t)) d t $$

Evaluate the given indefinite integral. $$ \int\left(t^{2}+3\right)\left(t^{3}-2 t\right) d t $$

Evaluate the definite integral. $$ \int_{0}^{1} x^{100} d x $$

Evaluate the given indefinite integral. $$ \int x^{2} x^{3} d x $$