Problem 254E: Why is u-substitution referred to as change of variable? Problem 255E: . If f=gh , when reversing the chain rule, ddx=(gh)=g(h(x))h(x) , should you take u=g(x) or u=h(x) ? Problem 256E: In the following exercises, verify each identity using differentiation. Then, using the indicated... Problem 257E: In the following exercises, verify each identity using differentiation. Then, using the indicated... Problem 258E: In the following exercises, verify each identity using differentiation. Then, using the indicated... Problem 259E: In the following exercises, verify each identity using differentiation. Then, using the indicated... Problem 260E: In the following exercises, verify each identity using differentiation. Then, using the indicated... Problem 261E: In the following exercises, find the antiderivative using the indicated substitution. 261. (... Problem 262E: In the following exercises, find the antiderivative using the indicated substitution. 262. (... Problem 263E: In the following exercises, find the antiderivative using the indicated substitution. 263. (... Problem 264E: In the following exercises, find the antiderivative using the indicated substitution. 264. (... Problem 265E: In the following exercises, find the antiderivative using the indicated substitution. 265. x x 2... Problem 266E: In the following exercises, find the antiderivative using the indicated substitution. 266. x 1 x 2... Problem 267E: In the following exercises, find the antiderivative using the indicated substitution. 267. (x1)( x 2... Problem 268E: In the following exercises, find the antiderivative using the indicated substitution. 268. (x22x)( x... Problem 269E: In the following exercises, find the antiderivative using the indicated substitution. 269.... Problem 270E: In the following exercises, find the antiderivative using the indicated substitution. 270.... Problem 271E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 272E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 273E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 274E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 275E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 276E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 277E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 278E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 279E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 280E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 281E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 282E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 283E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 284E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 285E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 286E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 287E: In the following Exercises, use a suitable change of variables to determine the indefinite integral.... Problem 288E: In the following Exercises, use a calculator to estimate the area under the curve using left Riemann... Problem 289E: In the following Exercises, use a calculator to estimate the area under the curve using left Riemann... Problem 290E: In the following Exercises, use a calculator to estimate the area under the curve using left Riemann... Problem 291E: In the following Exercises, use a calculator to estimate the area under the curve using left Riemann... Problem 292E: In the following exercises, use a change of variables to evaluate the definite integral. 292.... Problem 293E: In the following exercises, use a change of variables to evaluate the definite integral. 293. 01x 1+... Problem 294E: In the following exercises, use a change of variables to evaluate the definite integral. 294. 02t 5... Problem 295E: In the following exercises, use a change of variables to evaluate the definite integral. 295. 01t 1+... Problem 296E: In the following exercises, use a change of variables to evaluate the definite integral. 296.... Problem 297E: In the following exercises, use a change of variables to evaluate the definite integral. 297. 0/4sin... Problem 298E: In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using... Problem 299E: In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using... Problem 300E: In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using... Problem 301E: In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using... Problem 302E: In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using... Problem 303E: In the following exercises, evaluate the indefinite integral f(x)dx with constant C = 0 using... Problem 304E: If h(a)=h(b) in abg(h(x))h(x)dx , what can you say about the value Elf the integral? Problem 305E: Is the substitution u=1x2 02x1x2dx okay? If not, why not in the definite integral Problem 306E: In the following exercises, use a change of variables to show that each definite integral is equal... Problem 307E: In the following exercises, use a change of variables to show that each definite integral is equal... Problem 308E: In the following exercises, use a change of variables to show that each definite integral is equal... Problem 309E: In the following exercises, use a change of variables to show that each definite integral is equal... Problem 310E: In the following exercises, use a change of variables to show that each definite integral is equal... Problem 311E: In the following exercises, use a change of variables to show that each definite integral is equal... Problem 312E: In the following exercises, use a change of variables to show that each definite integral is equal... Problem 313E: Show that the avenge value of f(x) over an interval [a, b] is the same as the average value of f(cx)... Problem 314E: €314. Find the area under the graph of f(t)=t(1 t 2)a between t = 0 and t = x where a > 0 and a1 is... Problem 315E: Find the area under the graph of g(t)=t(1 t 2)a between t = 0 and t = x, where 0 < x < 1 and a > 0... Problem 316E: The area of a semicircle of radius 1 can be expressed as 111x2dx . Use the substitution x = cost to... Problem 317E: The area of the top half of an ellipse with a major axis that is the x-axis from x = l to a and with... Problem 318E: [T] The following graph is of a function of the form f(t)=asin(nt)+bsin(mt) . Estimate the... Problem 319E: The following graph is of a function of the form f(x)=acos(nt)+bcos(mt). Estimate the coefficients a... format_list_bulleted