Calculus Answers

Coordinate axes, the curve y = sin (x) and the straight line x = 3π/2 limit one area.
Determine the size of this area.

If velocity ,time and force were chosen as basic quanties ,find the dimensions of mass

EVALUATE ∫dx/(1+2cosx)

LOWER LIMIT 0
UPPER LIMIT PI/2

Find the point of inflexion of the curve.

The car's speed after braking is v (t) = 16.9 - 0.1t2 (where time t is seconds).

a) How long does the braking last?

(b) the distance traveled by the first 3 and last 3 cars
within seconds of starting braking?

c) How long does the car move during the entire braking?

1. Calculate the numerical value of the following integral
∫_(-4)^2[(2-x^2 )-(3x+2)] dx

2. Calculate the curves f (x) = 2 - x2 and g (x) = 3x + 2 total area A between [-4,2]. Compare to the previous problem 1. and notice that there will be a different answer to these! Why came a different answer?

1. Integrate with the placement method: ∫cosxsin2xdx

2. Integrate using the partial integration method
a.) ∫e^x*cosx dx
b.) ∫x^2*e^3x dx

Integrate using the fractional fracture development (point b). For a and c, first divide by the division angle.

a.) ∫3x2+2x+2/x-3 dx

b.) ∫3/x2-1 dx

c.) ∫2x2+x/x+2 dx

x^2/3+y^2/3=a^2/3 , a>0 (astroid) rotate about y-axis and find the volume?