Indefinite Integration Questions and Answers

Find f such that f x f x 7 x f 16 62

5 Evaluate the following trigonometric integral Identify which case number from the Lecture 3 notes the integral falls under 4 points

1 Differentiate a f x esinx e f x ln 6x the following functions Do not forget to use the chain rule 10 Points b f x 7x c f x log2 4x 2 d f x arctan 7x

N D La C Find the integral 6x 5 dx Hint Expand first 6x 5 dx

N Di La Ci At Next question Solve the following integral The answer can be determined by rules of antidifferentiation but some algebra may be required beforehand u7 4u5 9 du u7 4u5 9 0 du

a At Use the form 12x dx f12 dx faxd a dx 1 In a C to solve the following indefinite integral

For the Periodic triangle function X t ANAL 1 2 Test 3 Parseval s relation i e Calulate 2 S xlt 1 dt and lac lael 2

3 If f1 x 8x cos x and 6 find 7 O 2 2 6 O 2 2 6 08 O 0 O 2 2

t T Find an exponential function of the form P t Pon that models the situation and then find the equivalent exponential model of the form P t Poet Doubling time of 4 yr initial population of 500 T Find an exponential function of the form P t Pon that models the situation The exponential function is P t Use integers or fractions for any numbers in the expression

0 8 0 6 0 4 0 2 2 3 2 5 8 Use Newton s method to approximate a root of the equation cos Enter your root with at least 5 decimal places Use Newton s method to approximate a root of the equation cos z 4 x as follo

nd the Intervals of convergence of f x t x 7 x and f x 1 1 x 6 n n 1 0 x b x C F x d x dx r x dx f x dx Enter your answer using interval notation Be sure to check for convergen

Use substitution to find the indefinite integral x5 6 X S x 36x 2 3 dx x5 6 S 10 dx 2 3 x 36x

dt Evaluate the indefinite integral cos t 8 9 tan t Only use methods taught in lecture

Evaluate the integral Only use methods taught in lecture Show full work justify fully ft7 In t dt

5 pts Evaluate the integral Only use methods taught in lecture Show full work justify fully fi In 1 dt

Integrate assuming x 0 xin 4x dx S x In 4x dx

Use substitution to find the given indefinite integral 7 dx 6 8x

10 Find the derivative of the function g x t sin t dt Only use methods taught in lecture x Show full work and explain each step

Evaluate the indefinite integral work justify fully dx Only use methods taught in lecture Show full 1 x8

Suppose the supply function of a certain item is given by S aq and the demand function is given by D q Complete parts a through d 7 1 S q 9 1 D q 10 9 19 a Graph the supply and demand curves Use the graphing tool to graph the functions Click to enlarge graph b Find the equilibrium point Type an ordered pair c Find the consumers surplus Type an integer or a decimal d Find the producers surplus CHITE 20 18 16 14 12 10 B 6

Use substitution to find the given indefinite integral 6 11 7x 6 dx 11 dx

Use substitution to find the indefinite integral S x 4 7 x 4 x 28x 2 3 dx 2 3 dx

Use substitution to find the given indefinite integral x 7x 3 dx xx 78 3 dr dx

Select the correct answer below f x 4 3 Of x 2 5 O f x 4 8 Of x 4 Of x 7 5 28 24 20 16 12 8 2

The graph of the acceleration a t of a car measured in ft s is shown below Use Simpson s rule with n 6 to estimate the increase in the velocity in ft s of the car during the 6 second time interval Round your answer to two decimal places ak 12 8 4 0 ft s 2 4 6 t seconds

Use Simpson s Rule with n 10 to estimate the arc length of the curve Round your answer to four decimal places y e x 0 x 4 Find the answer produced by a calculator or computer to compare with the previous result Round your answer to four decimal places

Evaluate the indefinite integral 4x 3 4x 6x 2 dx

Evaluate the indefinite integral 2 2 x5dx

Find the general antiderivative of f x 4x6 6 1 5 x X x6

d the particular solution for the equation dy 4x 9x x y 0 when x 2 dx

Suppose that 4 J of work is needed to stretch a spring from its natural length of 26 cm to a length of 41 cm a How much work in J is needed to stretch the spring from 28 cm to 33 cm Round your answer to two decimal places 0 80 J b How far beyond its natural length in cm will a force of 30 N keep the spring stretched Round your answer one decimal place 67 07 X cm

A tank is full of water Find the work in ft lb required to pump the water out of the spout Use the fact that water weighs 62 5 lb ft 13006339 5 T 7 ft 12 ft X ft lb Need Help Read It

Each antiderivative of nth degree polynomial function is an n 1 th degree polynomial function True False

The graph of an exponential function has a y intercept of 10 and contains the point 2 160 Construct the function that describes the graph holow

Find the sum of the convergent series 12 00 n 1 16 n n 2

Find the general solution for the differential equation 3y dx Choose the correct answer below O A OB O C O D y C 9x 16 y y 16x 9 16x 9 9x3 16 C C dy 8x C

Shown is the graph of a force function in newtons that increases to its maximum value and then remains constant F N 24 18 12 6 3 6 9 12 15 18 21 24 x m How much work W is done in J by the force in moving an object a distance of 24 m W J

Evaluate the integral Use C for the constant of integrati 13z e dz

What is the general anti derivative of f x 3 2x 10 O F x x 5 C O F x 2x 10 C O F x 2x 10 C O F x x 10 C

Use substitution to find the indefinite integral 3x 7x dx

9 Solve the differential equation df du 16u 9u 16 u

0 Find the indefinite integral of the following function 5 1 t t

nd the indefinite integral Sz 5 z dz

3 Find the indefinite integral 58 85 15 ds 54

2 Find the indefinite integral 6u 4 du

1 Find the general solution of the differential equation below 3 dy 9 ds 75

Solve by substitution f 8x7 e4x dx 8

Use integration by parts to find the integral f x 4 In x dx OA 2x Inx 4xInx 4x C OB Inx x C O C Inx x 4x C OD Xnx C Inx x C

Use substitution to find the indefinite integral Sax 2x dx

Evaluate the integral 6e6t So 7 e6t 6e6t dt dt