Problem 126E: Simplify the following expressions by writing each one using a single trigonometric function. 126.... Problem 127E: Simplify the following expressions by writing each one using a single trigonometric function. 127.... Problem 128E: Simplify the following expressions by writing each one using a single trigonometric function. 128.... Problem 129E: Simplify the following expressions by writing each one using a single trigonometric function. 129.... Problem 130E: Simplify the following expressions by writing each one using a single trigonometric function. 130.... Problem 131E: Use the technique of completing the square to express each trinomial as the square of a binomial.... Problem 132E: Use the technique of completing the square to express each trinomial as the square of a binomial.... Problem 133E: Use the technique of completing the square to express each trinomial as the square of a binomial.... Problem 134E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 135E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 136E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 137E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 138E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 139E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 140E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 141E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 142E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 143E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 144E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 145E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 146E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 147E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 148E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 149E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 150E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 151E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 152E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 153E: Integrate using the method of trigonometric substitution. Express the final answer in terms of the... Problem 154E: In the following exercises, use the substitutions x=sinh , cosh , or tanh . Express the final... Problem 155E: In the following exercises, use the substitutions x=sinh , cosh , or tanh . Express the final... Problem 156E: In the following exercises, use the substitutions x=sinh , cosh , or tanh . Express the final... Problem 157E: In the following exercises, use the substitutions x=sinh , cosh , or tanh . Express the final... Problem 158E: In the following exercises, use the substitutions x=sinh , cosh , or tanh . Express the final... Problem 159E: In the following exercises, use the substitutions x=sinh , cosh , or tanh . Express the final... Problem 160E: Use the technique of completing the square to evaluate the following integrals. 160. 1x26xdx Problem 161E: Use the technique of completing the square to evaluate the following integrals. 161. 1x2+2x+1dx Problem 162E: Use the technique of completing the square to evaluate the following integrals. 162. 1 x 2 +2x+8dx Problem 163E: Use the technique of completing the square to evaluate the following integrals. 163. 1 x 2 +10xdx Problem 164E: Use the technique of completing the square to evaluate the following integrals. 164. 1 x 2 +4x12dx Problem 165E: Evaluate the integral without using calculus: 339x2dx Problem 166E: Find the area enclosed by the ellipse x24+y29=1 . Problem 167E: Evaluate the integral dx 1 x 2 using two different substitutions. First, let x=cos and evaluate... Problem 168E: Evaluate the integral dxx x 2 1 using the substitution x=sec . Next, evaluate the same integral... Problem 169E: Evaluate the integral xx2+1 using the form 1udu . Next, evaluate the same integral using x=tan . Are... Problem 170E: State the method of integration you would use to evaluate the integral xx2+1dx . Why did you choose... Problem 171E: State the method of integration you would use to evaluate the integral x2x21dx . Why did you choose... Problem 172E: Evaluate 11xdxx2+1 Problem 173E: Find the length of the arc of the curve over the specified interval: y=Inx , [1,5] . Round the... Problem 174E: Find the surface area of the solid generated by revolving the region bounded by the graphs of y=x2 ,... Problem 175E: The region bounded by the graph of f(x)=11+x2 and the x-axis between x=0 and x=1 is revolved about... Problem 176E: Solve the initial-value problem for y as a function of x. 176. (x2+36)dydx=1 , y(6)=0 Problem 177E: Solve the initial-value problem for y as a function of x. 177. (64x2)dydx=1 , y(0)=3 Problem 178E: Solve the initial-value problem for y as a function of x. 178. Find the area bounded by y=2644x2 ,... Problem 179E: An oil storage tank can he described as the volume generated by revolving the area bounded by... Problem 180E: During each cycle, the velocity v (in feet per second) of a robotic welding device is given by... Problem 181E: Find the length of the curve y=16x2 between x=0 and x=2 . format_list_bulleted