Answer Key
837
4
⎛ ⎝ x 2 −2 x ⎞ ⎠
267 . 1 8
+ C
3 θ 3 +
269 . sin θ − sin
C
101 101 −
(1− x ) 100
271 . (1− x )
C
100 +
273 . ⌠
⌡ (11 x - 7) -2 dx=− 1
+ C
22(11 x −7) 2
4 θ 4 + 3 ( πt ) 3 π
275 . − cos
C
277 . − cos
+
C
2 ⎛
⎞ ⎠ + C
⎝ t 2
279 . − 1 4 cos 281 . − 1
+ C
3( x 3 −3) ⎞ ⎠ 3 1− y 3 2 ⎛ ⎝ y 3 −2
283 . −
11
⎛ ⎝ 1−cos 3 θ ⎞ ⎠
285 . 1 33 287 . 1 12
+ C
4
⎛ ⎝ sin 3 θ −3sin 2 θ ⎞ ⎠ + C 289 . L 50 =−8.5779. The exact area is −81 8 291 . L 50 = −0.006399 … The exact area is 0. 293 . u =1+ x 2 , du =2 xdx , 1 2 ∫ 1 2
u −1/2 du = 2−1
295 . u =1+ t 3 , du =3 t 2 dt , 1 3 ⌠ ⌡ 1 2 297 . u =cos θ , du =−sin θdθ , ⌠ ⌡
u −1/2 du = 2 3
( 2−1)
1/ 2 1
u −4 du = 1 3
(2 2−1)
299 .
The antiderivative is y = sin ⎛
⎝ ln(2 x ) ⎞ ⎠ . Since the antiderivative is not continuous at x =0, one cannot find a value of C that
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