91Ó°ÊÓ

In Exercises \(11 - 14 ,\) use NINT to find the average value of the function on the interval. At what point (s) in the interval does the function assume its average value? $$y = - \frac { x ^ { 2 } } { 2 } , \quad [ 0,3 ]$$

In Exercises 13-18, (a) use Simpson's Rule with n = 4 to approximate the value of the integral and (b) find the exact value of the integral to check your answer. (Note that these are the same integrals as Exercises 1-6, so you can also compare it with the Trapezoidal Rule approximation.) $$\int_{0}^{2} x d x$$

In Exercises \(11 - 14 ,\) use NINT to find the average value of the function on the interval. At what point (s) in the interval does the function assume its average value? $$y = - 3 x ^ { 2 } - 1 , [ 0,1 ]$$

In Exercises \(1-20,\) find \(d y / d x\). $$y=\int_{x}^{0} \ln \left(1+t^{2}\right) d t$$

In Exercises \(11 - 14 ,\) use NINT to find the average value of the function on the interval. At what point (s) in the interval does the function assume its average value? $$y = ( x - 1 ) ^ { 2 } , \quad [ 0,3 ]$$

In Exercises \(1-20,\) find \(d y / d x\). $$y=\int_{x}^{7} \sqrt{2 t^{4}+t+1} d t$$

In Exercises 13-18, (a) use Simpson's Rule with n = 4 to approximate the value of the integral and (b) find the exact value of the integral to check your answer. (Note that these are the same integrals as Exercises 1-6, so you can also compare it with the Trapezoidal Rule approximation.) $$\int_{0}^{2} x^{2} d x$$

In Exercises \(1-20,\) find \(d y / d x\). $$y=\int_{x^{3}}^{5} \frac{\cos t}{t^{2}+2} d t$$

In Exercises 13-18, (a) use Simpson's Rule with n = 4 to approximate the value of the integral and (b) find the exact value of the integral to check your answer. (Note that these are the same integrals as Exercises 1-6, so you can also compare it with the Trapezoidal Rule approximation.) $$\int_{0}^{2} x^{3} d x$$

In Exercises \(1-20,\) find \(d y / d x\). $$y=\int_{5 x^{2}}^{25} \frac{t^{2}-2 t+9}{t^{3}+6} d t$$