1. Determine the value of f(x)=-5x^3+7x on [-1,2]. 2. Determine the area of region bound by f(x)=-2x^2+x+6 and the x-axis on [0,3]. 3. Determine the area of the region bounded by f(x)=x^2 - 4 and g(x)=x+2 4. Determine the area of the region bounded by f(x)=x+6 and g(x)=-x^2+2 on the interval on [-2, 2]. keywords:
I have a double integral of the form I from 0 to 2 and I from 0 to y (4-y^2) dx dy How does one convert this double integral into a triple integral? keywords: integration, integrates, integrals, integrating, double, triple, multiple
Find the area under the normal curve which is shaded on the graph. Use 4 decimal places. See attached file for full problem description.
(See attached file for full problem description). Please help with 7C, 10 and 12 7. Find the integral... 10. A beacon on a lighthouse 2000 m away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 m fr
If X(c,d) is the function from into such that X(c,d)(x)={1 if xE(c,d) and (c,d)⊂[a,b], show that ∫a-->b Xc,d =d-c. {0 otherwise Please see the attached file for the fully formatted problem.
If and are functions from to which are Riemann integrable on and which differ at only a finite number of points in , show that . Please see the attached file for the fully formatted problems.
Let f be a function from R^n to R which is bounded on [a,b]. Show that f is Riemann integrable on [a,b] if and only if for each epsilon>0 there is a partition P such that U(f,P)-L(f,P)<epsilon. note U(f,P)=upper sum L(f,P)=lower sum
Consider the nonlinear Fredholm equation where is continuous on [a,b] and is continuous and satisfies a Lipschitz condition: on the set . Show that the integral equation has a unique solution on [a,b] if .
4 A) Evaluate ∫ 6x(2x^2 - 1) dx 2 b) Write down a definite integral that will give the value of the area under the curve y=x^3 cos (1/4 x) between x=pi and x=2pi pi=3.142 (you are not asked to evaluate the integral by hand) c) use mathcad to find the area described in part b,
Integration: Motion in a straight line. See attached file for full problem description.
Please see the attached file for the fully formatted problems.
Please see the attached file for the fully formatted problems. keywords: integration, integrates, integrals, integrating, double, triple, multiple keywords: finding, solve, solving, evaluate, evaluating, verify, verifying
Find the indefinite integral of the following function. g(x)= 19+15^3/x
(See attached file for full problem description).
(See attached file for full problem description) Assume that f is continuous on Reals and periodic with p. Show that for any a.
Find the indefinate integrals off the following functions: f(t) = 2cos(4t) - 3e^5t g(x) = (19+15x^3)/ x (x>0) h(u)= sin^2[(1/10)u] I'm struggling to understand these questions so if someone could write a/n solution/explanation for them that would be great.
(See attached file for full problem description with proper symbols) --- Assume that f is continuous on [a,b], g is differentiable on [c,d], g([c,d]) [a,b] and F(x) = For each x [c,d]. Prove that F'(x)=f(g(x))g'(x) For each x (c,d). ---
(See attached file for full problem description) --- Assume that f is continuous on [a,b] and f(x) 0 for each x [a,b]. Prove that >0 if there exists c (a,b) such that f(c)>0.
Please see the attached file for the fully formatted problems. keywords: finding, solve, solving, evaluate, evaluating, verify, verifying keywords: integration, integrates, integrals, integrating, double, triple, multiple
1. The United States Census Bureau mid-year data for the population of the world in the year 2000 was 6.079 billion. Three years later, in 2003, it was 6.302 billion. Answer the following questions. (See attached bmp file) 2. A metal ball, initially at a temperature of 90 C, is immersed on a large body of water at a temperat
(See attached file for full problem description with proper equations) Evaluate these: 1. Find dw/dx for the function given by w=xye^(xyz) 2. Find the center and radius of the sphere given by the equation x^2 + y^2 + z^2 + 4x - 2y + 2z=10 3. The sum of $2000 is deposited in a savings account earning r percent int
Integrate: cos^2 theta. keywords: integration, integrates, integrals, integrating, double, triple, multiple, trig
Application of Residue theorem. See attached file for full problem description.
Create an integral whereby you are forced to use all four types of integration. Work the problem and explain why each (u-substitution, trig substitution, fractions, parts) are all needed. this must be only one integral, that is it must all be under a singular fraction and cannot be the sum such as integral of lnx+arctanx dx or
Please provide in-depth evaluation of improper integrals using residues theorem.
(See attached file for full problem description) I tried solve this problem by following Cauchy's Residue Theorem. However, the answer is always wrong.
Evaluating the improper integrals using residues theorem. See attached file for full problem description.
I want to find the Cauchy value by using residues. (See attached file for full problem description)
A. Evaluate ∫ x(sqrt(x+1))dx B. Find the area bounded by y= x/(1+x)^2, y=0, x=0, and x=2 C. Evaluate ∫ 1/x(sqrt(x+9))dx D. Find the indefinite integral using integration by parts: ∫x^2(e^2x)dx Infinity Evaluate the improper integral: ∫ ln(x)dx
(See attached file for full problem description) 1. Calculate the values of the following integrals. 2. Write delta(x^2 - 4) in terms of a sum of ordinary delta functions. 3. Write delta(sin(x)) in terms of a sum of ordinary delta functions (an infinite number!). 4. Calculate the values of the following integrals inv