2nd Period review

Trigonometric Integrals

100

int (sin³(x)cos(x)dx)

sin⁴(x) / 4  +C

200

int(cot (33x) dx)

ln ( sin (33x)) / 33  +C

300

int (x³¹ sin (x³²) dx)

- cos (x³²) / 32 +C

400

int (cos x / sin¹⁴ (x)  dx)

- 1 / 13 sin¹³ (x) +C

500

int ( (sec (2x-56))² dx)

-tan (2x-56) / 2 +C

Logarithmic and exponential Integrals

100

int ( e^-8xdx)

- e^-8x / 8 +C

200

int (e^-x6(-6x⁵) dx)

e^-x6 +C

300

int (e^{cos 27x} sin(27x)dx)

-e^{cos 27x} / 27  +C

400

int (4^-x dx)

- 4^-x / ln (4)  +C

500

int (x⁶ 5^x7 dx)

5^x7 / 7ln (5) +C

Definite Integrals with Chain Rule

100

int (x²-4x+6)dx from 1 to 8

259/3 

200

int ( dx /cubic root ((8+4x)²)) form 0 to 14

3 / 2

300

int (x³(2x⁴+3)²dx)

49 / 12

400

int ( 6 cos (pi(x)/2 dx) from 0 to 1

12 / pi

500

int ( 1 / sqrt (3x +7) dx) from 3 to 6

2 / 3

Areas

100

Find the area between y=8x-x² and y=2x

A=36u²

200

Find the area between y=16-x² and y=x²-2

A=72u²

300

Find the area between y=x²+2x+3 and y=2x+7

A=2 u²

400

Find the area below y=16-x² and the x-axis

A=256/3 u²

500

Find the area below y=-4x+7 between [0,1]

A=5u²

Solids of rev

100

Calculate de volume of the solid obtained by revolving the region under de graph f(x)=x+3  over the interval [0,9]

V=567pi u³

200

Calculate de volume of the solid obtained by revolving the region under de graph f(x)=sqrt (x-1)  over the interval [0,7]

V=18 pi u3

300

Calculate de volume of the solid obtained by revolving the region under de graph f(x)=x+1  over the interval [0,2]

26 pi /3 u³

400

Calculate de volume of the solid obtained by revolving the region under de graph f(x)=2x+1  over the interval [0,3]

A=57 pi u³

500

Calculate de volume of the solid obtained by revolving the region under de graph f(x)=2sqrt (x+1)  over the interval [0,3]

V=18 pi u³