Calculus Volume 1

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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