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Indefinite Integral - AP Calculus - Practices Problems, Exercises of Calculus

Birla Institute of Technology and ScienceCalculus

This lecture is from AP Calculus. Key important points are: Indefinite Integral, Trignometric Problems, Exponential Fractions, Summation, Differential Equation

Typology: Exercises

2012/2013

Uploaded on 01/31/2013

ekavia
ekavia 🇮🇳

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Calculus Ch. 4 Name_________________________
Worksheet 4.1 – 4.4
Evaluate the indefinite integral.
1.
x
2
+3x +2
x
3
dx
∫
2.
3w – 2
( )2dw
∫
3.
x
5
+sec
2
x
( )
dx
∫
4.
2cscx cotx dx
∫
Solve the differential equation.
5.
′′
f (x) =x+4, ′
f (1) =2, and f (1) =5
Use the properties of summation to evaluate the sum.
6.
( )
20 2
i1
i1
=
+
∑
7.
( )
12 2
i1
i 3i 2
=
−
∑
pf3
pf4

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Calculus Ch. 4 Name_________________________ Worksheet 4.1 – 4.

Evaluate the indefinite integral.

x 2 + 3x + 2 (^3) x

^

∫ dx 2.^ (3w – 2^ )

2

∫ dw

3. ∫ (x 5 + sec 2 x)dx 4. ∫2 csc x cot x dx

Solve the differential equation.

  1. f (x)′′ = x + 4, f (1)′ = 2, and f(1) = 5

Use the properties of summation to evaluate the sum.

(^20 )

i 1

i 1

∑ + 7.^ (^ )

12 2 i 1

i 3i 2

Use the limit process to find the area of the region between the graph of the function and the x-axis over the given interval.

8. y = 8 − 2x, [1,3 ] 9. y = x 2 +3, [ 0, 2]

Set up a definite integral that yields the area of the region. Do not find the area.

  1. f(x) =

x 2 + 3 11. f(x) = cos x

Sketch the region whose area is indicated by the definite integral. Then use a geometric formula to evaluate the integral.

(^4 ) ∫ 0 16 – x^ dx 13.^ (^ )

3 ∫ 0 2x^ +1 dx

Use the Fundamental Theorem of Calculus to evaluate the integrals.

3 ∫ (^) − 1 3x^ +4 dx

3 1 3

dx ∫ x

3 2

π (^5) 2

π − 2 2

  1. A demographic study indicates that the population of a certain town is growing at the rate of

4 + 2x 0.8^ people per month when x is time in months. What will be the increase in population between

the 10th and 12th months?

  1. The volume V in liters of air in the lungs during a 5-second respiratory cycle is approximated by the

model: V = 0.1729t + 0.1522t 2 – 0.0374t 3 where t is the time in seconds. Approximate the average volume of air in the lungs during 1 cycle.

  1. A rare stamp is appreciating at the rate of 5 + .5t in thousands of dollars per year when t is measured in years. If this stamp is purchased for a newborn baby and allowed to appreciate, what will be the value of the stamp on the child's 18th birthday?