Cal 2 Test 2

Exponentially Cooked

Feelin' inDifferent

Triple Trig Trouble

Partial Parts

Hell Scraps

100

Evaluate the integral

1/x dx from -3 to -2

ln(2/3)

100

Evaluate the differential eqution

dy/dx = e^x-y

What is

y=ln(e^x+C)

100

Evaluate the integral

sin³x dx

What is cos³x/3 - cosx +C

100

Expand the quotients by partial fractions

(5x-13) / ((x-3)(x-2))

What is

2/(x-3) + 3/(x-2)

100

Evaluate the integral

1 / sqrt(1 - x²) from 0 to 1

What is π/2

200

Evaluate the integral

e^sqrt(r) / sqrt(r) dr

What is 2e^sqrt(r)+C?

200

Solve the differential equation

sqrt(2xy) dy/dx = 1

What is

y = (3/2(sqrt(2)x^3/2+C))^2/3

200

Evaluate the integral

sin³x cos³x dx

What is

cos⁶x / 6 + cos⁴x / 4 + C

200

Evaluate the integral

4x cos(2-3x)

What is

(-4x/3) sin(2-3x) + (4/9)cos(2-3x) + C

200

Evaluate the integral

x lnx from 0 to 1

What is -(1/4)

300

Evaluate the integral

x2^{x^2} from 1 to sqrt 2

What is 1/ln2?

300

Solve the differential equation

y² dy/dx = 3x²y³ - 6x²

What is

y= (Ae^{3x^3}+2)^1/3

300

Evaluate the integral

sec²x tanx

What is

tan²x / 2 +C

300

Express the integrand as sum of partial fractions and evaluate the integrals

(x+4) / (x²+5x+6)

What is

(2/7) ln| x + 6 | + (5/7) ln|x- 1| + C

300

Evaluate the integral

θe^θfrom -∞ to 0

What is -1

400

Evaluate the integral

log₂x / x from 1 to 4

What is 2(ln4)^2 / ln(2)

400

Solve the differential equation

sec(x) dy/dx = e^{y + sinx}

What is

y = -ln(-e^sinx-C)

400

Evaluate the integral

sqrt( 1 - cos2x) from 0 to π

What is

2 sqrt(2)

400

Evaluate the integral

e^θcosθ

What is

(1/2) ( e^θcosθ + e^θsinθ) + C

400

Evaluate the integral

(s+1) / sqrt(4 - s²)

What is π / 2 + 2

500

Evaluate the integral

e^{(-1/x^2)} / x³

What is -(1/2)e^{-(1/x^2)}+C

500

Solve the differential equation

dy/dx = e^x-y + e^x + e^-y + 1

What is

y = ln(Ae^{e^x + x} -1)

500

Evaluate the integral

sqrt(1 - 9t²)

What is

(1/2)sqrt(1-9t²) + (1/6)sin^-1(3t) +C

500

Express the integrand as a sum of partial fractions and evaluate the integrals

(y²+2y+1)/(y²+1)²

What is

arctan(y) - 1/(y²+1) + C