Definite Integrals Questions and Answers

Find the consumer s surplus for the following demand function at the given point 3 D x x 3 x 4 33 7 28 3 25 4 50

Find the area lying above the x axis and under the parabola y 4x x Round answers to three decimal places 10 667 11 10 667 32

Set up a definite integral that represents the shaded area y h x 9 8 a S 4 h x 3 2 1 9 of 0 of 0 2 h x dx OS h x dx 3 3 h x dx 2 h x dx 4 5 6 7 8 9 x

ven function f to answer par log x 2

3 Compute the value of the iterated integral 1 f dxf dye

Draw the graph of f x 6 5 10 Clear All Draw 7 987 9 8 7 6 5 4 3 2 10 9 8 7 6 5 4 3 2 1 7 77774 999 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Apply the method of undetermined coefficients to find a particular solution to the following system x 7x 10y 12 y 2x 5y 3e

10 x y and above the cone 7 Find the exact volume of the solid that is below the hemisphere z z 2 x y by setting up a triple integral using spherical coordinates 16 pts

HomeworkC3S2 Question 4 of 8 1 point Question Use the function below to answer the foll g x 3 5 a Use transformations of the graph of y b Write the domain and range in interv c Write an equation of the asymptote Part 0 3 Part 1 of 3 a Use transformations of the graph c

Use the following information to answer each question below Estimate any irrational answers to one deci place The chemistry test scores of 9 students were recorded as follows 100 84 91 77 69 92 93 93 88 18 Find the mean and range of the chemistry test scores 19 Find the median and mode of the chemistry test scores 20 Find the standard deviation of the chemistry test scores 84

Select the answer for the following question 21 If m x 2 x and min x 18 then n x 1 B 81x D 9x E 9x C 629

8 Let N t denote the size of a population at time t and assume that dN dt f t Express the cumulative change of the population size in the in terval 0 3 as an integral

Find the center of mass of the solid S bounded by the paraboloid z 3x 3y and the plane z 11 Assume the density is constant Hint Think about the shape before calculating you can greatly reduce the number of calculations to be

In a design for the Tower of Babel with an infinite height in order to reach the heavens the horizontal cross sections are circles with the radius as a function of height given by the equation r f h frac h left h 3 a right a If there is 4 cubic kilometres of material available for the construction of the tower find the value that the parameter a must take b The number of days per kilometre of height d that it takes to build a section of the tower depends on the cross sectional area and the steepness of the sides according to the function d g h frac pi f h 2 f prime h Find an explicit expression for this function c Use the function d g h to find the time it would take to build the entire tower if it exists

C MATH1507 M N O P utorial Assignments an

Exercice III 10 Points Find the Fourier series of the function if 0 x if x T f x X

Rewrite cos x 5TT 4 in terms of sin x and cos x

3 2 13 12 11 10 0 8 7 6 5 4 3 2 1 1 f m 2 3 6 a The curve above is the graph of a sinusoidal function It goes through the points 7 2 and 3 2 Find a sinusoidal function that matches the given graph If needed you can enter 3 1416 as pi in your answer otherwise use at least 3 decimal digits

Write an iterated integral of a continuous function f over the region R shown in the figure Write an iterated integral of a continuous function f SS f x y dx dy 25 20 15 10 www Ay 15 73910 Q

Write a single iterated integral of a continuous function f over the following region The region bounded by the triangle with vertices 0 0 32 0 and 16 4 S S X Y

Consider the region R shown in the figure and write an iterated integral of a continuous function f over R Choose the correct iterated integral below O A 6x 6 fff x y 0 f x y dx dy OB 6 6x SS FO 0x2 f x y dx dy 8 CO O C 6 6x SS f x 0x f x y dy dx Ay J y x O D 6 y 6x 6x 0 Q f x y dy dx

Evaluate the following line integral along the curve C X 2 X ds where C is the line segment from 1 1 to 10 10 2 y The value of the integral is Type an exact answer using radicals as needed

Find the average value of the following function on the given curve f x y x 2y on the line segment from 1 1 to 2 7 The average value of f x y on the given curve is Simplify your answer

Sv 4x 5y 3y 0 6x 3y 4 4x 5y 1 4x 5y 2 nd 6x 3y dA where R is the parallelogram enclosed by the line

nline Assignments Assignment 2 stion 9 vet ered ed out of ag question Evaluate the following inte given that

Evaluate d dx 4x4 fe 2 t t 6 dt

A function y f x passes through P 3 15 and Q 3 30 Let the function g x f 3x The transformation that maps the graph off x to the graph of g x maps point P to P and point Q to Q where P a b and Q c d are given Write down the values of a b c d E Z in the order given here 184x2 55

Use the washer method to find the volume of the solid generated when the region bounded by y 2x and y 4 x is revolved about the x axis OA Ody B JOdx YA Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers y 4 x RY 2x

0 5 1 COS X x Evaluate the integral 0 5 da correct up to 4 decimal plac

Evaluate the following integral in spherical coordinates The integral calculates the volume a R6 9 SS S p sin p dp de de 0 0 3 sec p 6 6 9 iii 0 0 3 sec p sin o dp do de or using as needed H

1 Give the domain and range of each of the following functions 6 pts function sin x arcsin x cos x x arccos x tan 1 x arctan x domain range

Evaluate the following integral in spherical coordinates 2 T 4 2 csc S S S p sin op dp dp de 0 6 0 2 4 2 csc 2 SS S p sin o dp do de 0 6 0 Type an exact answer using it as needed

Evaluate the following integral in cylindrical coordinates 6 36 x 2 s s 0 0 2 S 0 6 36 x x y 2 x y x y 1 2 dz dy dx S S S x y 0 0 0 Type an exact answer using as needed x y 1 dz dy dx

Evaluate the following integral given that

Evaluate the following integral where R is the region in quadrants 1 and 4 bounded by the semicircle of radius 10 centered at 0 0 SS xy da n

Sketch the region of integration and evaluate the following integral 15x dA R is bounded by y 0 y 2x 4 and y x R Sketch the region of integration Choose the correct graph below OA Ay 10 Evaluate the integral 15x dA B 10 Ay Q

Evaluate the following integral where R is bounded by x 3 y 2x 4 and y x 2 SS v da R

Given the partition 1 2 5 7 the right endpoint Riemann sum for f x 1 on 1 7 is 3 f ck Ark k 1

Evaluate the following double integral over the region R by converting it to an iterated integral JS x 2y da 2y dA R x y 2 x 4 3 ys5 R A S x 2y dy dx 23 54 c ff x 2y dx dy 32 Evaluate the integral x 2y dA Type an exact answer SS 23 54 D ff x 2y 32 B x 2y dx dy x 2y dy dx

Evaluate the following iterated integral 31 31 00 foxy 00 6xy dx dy 6xy dx 6xy dx dy

Set up a definite integral that represent interval Compute answers to three de x y r and area r 9

Refer to the figure to the rig from a to b that represents

Refer to the figure to the right Set up a definite integral that represents the indicated shaded area over the interval b d Choose the correct answer below C OA S h x b d h x g x dx Oc fig x h x b h x dx b d OE h x g x dx fth x g x d a C OB Sig x h b d OD Sh x g x g x dx b C OF Sig x h b y h x y g x ab d x h x dx h x g x dx fth x g c d x h x dx h x g x a

Rewrite as an algebraic expression in terms of y Assume all angles are in Quadrant I sin cos y

Consider a circle with radius 19 that is centered at the origin Find the exact x and y coordinates of the point on this circle corresponding to an angle 315 C Y Remember to give exact answers using square roots if necessary

2 Use a change of variables to evaluate x y sin x y dA JR where R is the rectangle enclosed by the lines and x y 0 x y x y 0 x y 2

Let R be the lamina bounded by the lines y 0 and y x 3 and by the circles x2 y2 4 and x2 y2 9 If R has constant density 6 its center of mass is x y Findx and y

3 Converting the variables into polar coordinates evaluate 32 To the Sy 2 So 32 22 J x2 y2 dxdy

Identifying Functions State whether each graph represents a function 1 Ay 2 3 4 7 20 16 12 B 4 AY Ay 15 12 9 6 3 3 9 12 4 8 12 16 20 15 18 3 6 9 12 15 XA 5 8 27 24 21 18 15 12 9 6 3 20 16 12 8 20 16 12 8 8 12 16 20 Ay 16 112 15 12 9 6 3 y 8 414 42 12 6 y RA 8 12 16 20 SA 6 9 40 71 5 3 6 9 12 15 15 10 5 AY 40 35 30 25 20 15 10 5 Ay 30 25 20 45 4 5 10 8 10 12 14 16 15 20 Ay 9 415 18 10 10 15 20 25 30 35 x x

Separables Problem 3 1 point Use Euler s method with step size 0 25 to compute the approximate y values 91 92 93 and 4 of the solution of the initial value problem y 2 5x 4y y 1 3 V1 1 3 2 0 5 3 0 125 3 4 0 504