Jones Test 5

In-definition Integrals

100

Evaluate the following indefinite integrals:

∫ 6x⁵−18x²+7 dx

What is 

x⁶−6x³+7x+C

200

Evaluate the following indefinite integrals:

∫40x³+12x²−9x+14 dx

What is

10x⁴ + 4x³− 9/2 x² + 14x + C

300

 Evaluate 

∫w^-2 + 10w^-5 −8 dw

What is 

−w^-1−(5/2)w⁻⁴−8w+c

400

Evaluate 

∫(t²−1)(4+3t)dt

What is 

(3/4)t⁴+(4/3)t³−(3/2)t²−4t+c

500

Evaluate
∫2cos(w)−sec(w)tan(w)dw.

What is 

2sin(w)−sec(w)+c

Defined Integrals

100

Evaluate the integral

∫ 6x(x−1)dx from 0 to 1

What is -1

200

Evaluate

∫15w⁴−13w²+w dw from 3 to 0

What is -1233/2

300

Evaluate

∫7sin(t)−2cos(t)dt (from 0 to π/2)

What is 5

400

Evaluate

∫7e^y + 2/y dy from -5 to -2

What is 

7(e^-2-e^-5) + 2(ln(2)-ln(5))

500

Evaluate

∫e^x+1/(x²+1) dx from 0 to 2

What is 

e²+tan⁻¹(2)−1

Substituting Life

100

Evaluate

∫x³+e^(1/4)xdx from -1 to 2

What is 

15/4 + 4e^1/2 − 4e^−1/4

200

Evaluate 

∫8cos(2t) / (√9−5sin(2t)) dt from 0 to π/4

What is 8/5

300

Evaluate

∫4√(5+9t)+12(5+9t)⁷dt

What is

(1/9)[(8/3)(5+9t)^3/2+(3/2)(5+9t)⁸]+c

400

Evaluate 

∫ 6e^7w/(1−8e7w)³ +14e^7w / (1−8e^7w) dw.

What is 

−1/56(−3(1−8e^7w)⁻²+14ln∣∣1−8e^7w∣∣)+c

Curved Areas

100

Determine the area below f(x)=3+2x−x² and above the x-axis.

What is 32/3

200

Determine the area of the region bounded by y=x²+2, y=sin(x), x=−1 and x=2.

What is 9 + cos(2) - cos(1)

300

Determine the area of the region bounded by x=y²−y−6 and x=2y+4.

What is 343/6

400

Determine the area of the region bounded by y=1x+2, y=(x+2)², x=−3/2, x=1.

What is 

67/8−ln(1/2)−ln(3)