Calculus Answers

f(x)=3x+3y+sinxy+cosy

Double Integral

1. Integral from 0 to pi, Integral from 0 to y^2 of sin x/y dxdy

Double Integral

1. Integral from 0 to 3, Integral from 0 to 1 of 2x ( square root of x^2 +y dx dy

2. Integral from 0 to ln 3, Integral from 0 to 1 of xye^xy^2 dy dx

to calculate velocity of a car accelerating from rest in straight line. Equation is v(t) = A (1-e ^ -t/t max speed) the ^ means to the power of. v(t) is the instantaneous velocity of the car (m/s), t is the time in seconds, tmaxspeed is the time to reach the maximum speed in seconds and A is a constant. 1. Create a graph of acceleration vs time? 2. Apply the mathematical model which is a car with a t(0-28m/s) of 2.6s, a t(400m) of 10.46s in order to calculate the value of coefficient, maximum velocity and maximum acceleration?

Using the mathematical model: to calculate velocity of a car accelerating from rest in straight line. Equation is v(t) = A (1-e ^ -t/t max speed) the ^ means to the power of. v(t) is the instantaneous velocity of the car (m/s), t is the time in seconds, tmaxspeed is the time to reach the maximum speed in seconds and A is a constant. Find out how to 1. Create a graph of position vs time for the given model? 2. Derive an equation a(t) for the instantaneous acceleration of the car as a function of time. Identify the acceleration of the car at t=0s? and asymptote of this function as t ⮕ ∞?

Using the mathematical model: to calculate velocity of a car accelerating from rest in straight line. Equation is v(t) = A (1-e ^ -t/t max speed) the ^ means to the power of. v(t) is the instantaneous velocity of the car (m/s), t is the time in seconds, tmaxspeed is the time to reach the maximum speed in seconds and A is a constant. Questions: 1. Create a graph of velocity vs time for this model? 2. Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the value of x when t= 0s and then asymptote of this function as t ⮕ ∞?

Using the mathematical model: to calculate velocity of a car accelerating from rest in straight line. Equation is v(t) = A (1-e ^ -t/t max speed) the ^ means to the power of. v(t) is the instantaneous velocity of the car (m/s), t is the time in seconds, tmaxspeed is the time to reach the maximum speed in seconds and A is a constant. Find out how to: 1. Identify the units of the coefficient A, 2. physical meaning of A, 3. velocity of the car at t=0 and 4. asymptote of this function as t ⮕ ∞?

The velocity of the rocket after departure is directly proportional for some time
from the time of departure to the square root. Four seconds after departure
the rocket speed was 151.2 km / h. Calculate how high the rocket is at the time
t = 16 seconds? First, construct and integrate the rocket height equation
it. Remember that velocity v (t) = ds / dt, so that s = ∫

Integrate both points with the placement method:

a) ∫ x√x+1 dx

b) ∫ 2x/x2+1 dx

place a at position t = x + 1 and at position b = t = x2 + 1

Integrate with quotient development as needed. Tip: In a)
first, divide by, for example, a split angle.

a) ∫2x2-x+2/x-1dx

d) ∫x-1/x2-4dx