Indefinite Integrals

Calculus 1 / Ab

150 Practice Problems

06:11
Calculus of a Single Variable

Solving a Differential Equation In Exercises $7-10$ , find the general solution of the differential
equation and check the result by differentiation.
$\frac{d y}{d t}=9 t^{2}$

Integration
Antiderivatives and Indefinite Integration
02:24
Calculus of a Single Variable

Think About It Find the general solution of $f^{\prime}(x)=-2 x \sin x^{2}$

Integration
Antiderivatives and Indefinite Integration
Allan H.
02:56
Calculus of a Single Variable

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
$\int f(x) g(x) d x=\left(\int f(x) d x\right)\left(\int g(x) d x\right)$

Integration
Antiderivatives and Indefinite Integration
Allan H.
02:04
Calculus of a Single Variable

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $F(x)$ and $G(x)$ are antiderivatives of $f(x),$ then

$$F(x)=G(x)+C$$

Integration
Antiderivatives and Indefinite Integration
Allan H.
01:57
Calculus of a Single Variable

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
If $p(x)$ is a polynomial function, then $p$ has exactly one antiderivative whose graph contains the origin.

Integration
Antiderivatives and Indefinite Integration
Kenneth K.
03:05
Calculus of a Single Variable

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
Each antiderivative of an $n$ th-degree polynomial function is an $(n+1)$ th-degree polynomial function.

Integration
Antiderivatives and Indefinite Integration
Allan H.
03:39
Calculus of a Single Variable

Acceleration Assume that a fully loaded plane starting from rest has a constant acceleration while moving down a runway. The plane requires 0.7 mile of runway and a speed of 160 miles per hour in order to lift off. What is the plane's acceleration?

Integration
Antiderivatives and Indefinite Integration
Allan H.
05:17
Calculus of a Single Variable

Acceleration At the instant the traffic light turns green, a car that has been waiting at an intersection starts with a constant acceleration of 6 feet per second per second. At the same instant, a truck traveling with a constant velocity of 30 feet per second passes the car.
(a) How far beyond its starting point will the car pass the truck?
(b) How fast will the car be traveling when it passes the truck?

Integration
Antiderivatives and Indefinite Integration
Sherrie F.
22:28
Calculus of a Single Variable

Deceleration A car traveling at 45 miles per hour is brought to a stop, at constant deceleration, 132 feet from where the brakes are applied.

(a) How far has the car moved when its speed has been reduced to 30 miles per hour?
(b) How far has the car moved when its speed has been reduced to 15 miles per hour?
(c) Draw the real number line from 0 to $132 .$ Plot the points found in parts (a) and (b). What can you conclude?

Integration
Antiderivatives and Indefinite Integration
Allan H.
08:14
Calculus of a Single Variable

Acceleration The maker of an automobile advertises that it takes 13 seconds to accelerate from 25 kilometers per hour to 80 kilometers per hour. Assume the acceleration is constant.
(a) Find the acceleration in meters per second per seconds.
(b) Find the distance the car travels during the 13 seconds.

Integration
Antiderivatives and Indefinite Integration
Sherrie F.
05:41
Calculus of a Single Variable

A particle, initially at rest, moves along the $x$ -axis such thatits acceleration at time $t>0$ is given by $a(t)=\cos t .$ At time $t=0,$ its position is $x=3$

(a) Find the velocity and position functions for the particle.
(b) Find the values of $t$ for which the particle is at rest.

Integration
Antiderivatives and Indefinite Integration
Allan H.
03:36
Calculus of a Single Variable

A particle moves along the $x$ -axis at a velocity of $v(t)=1 / \sqrt{t}$ , $t>0 .$ At time $t=1,$ its position is $x=4 .$ Find the acceleration and position functions for the particle.

Integration
Antiderivatives and Indefinite Integration
Sherrie F.
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