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Magazine Problem 150
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{3}^{x} \sqrt{9-y^{2}} d y $$
Problem 151
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{4}^{x} \frac{d s}{\sqrt{16-s^{2}}} $$
Problem 152
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{x}^{2 x} t d t $$
Problem 153
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{0}^{\sqrt{x}} t d t $$
Problem 154
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{0}^{\sin x} \sqrt{1-t^{2}} d t $$
Problem 155
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{\cos x}^{1} \sqrt{1-t^{2}} d t $$
Problem 156
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{1}^{\sqrt{x}} \frac{t^{2}}{1+t^{4}} d t $$
Problem 157
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{1}^{x^{2}} \frac{\sqrt{t}}{1+t} d t $$
Problem 158
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{0}^{\ln x} e^{t} d t $$
Problem 159
In the following exercises, use the Fundamental Theorem of Calculus, Part 1 , to find each derivative. $$ \frac{d}{d x} \int_{1}^{e^{2}} \ln u^{2} d u $$
