1. Evaluate d/dx (t^3)/(1 + t^2) dt 2. Evaluate d/dx et^2 dt 3. Evaluate the indefinite integral ((t^2)sin(t) + 2sin(t))/(2 + y^2) + e^t dt 4. Evaluate the definite integral sqrt(t)(1 + t) dt 5. Evaluate the indefinite integral (2 - sqrt(x))^r dx 6. Evaluate the indefinite integral (1/x + 1/(x^4) + 1/(x^9) dx 7. Evaluate
Let f be a nonnegative integrable function. Show that the function F defined by F(x)= Integral[from -inf to x of f] is continuous by using the Monotone Convergence Theorem. From Royden's Real Analysis Text, chapter 4. See the attached file.
Show that if {see attachment} is a continuous random variable then ... Please see attachment for complete list of questions.
There is a rope that stretches from the top of Maidwell building to a tree on the racecourse, and the length of this rope is 1km. A worm begins to travel along the rope at the rate of 1cm each second in an attempt to get to the other end. then a strange thing happens... some malevolent deity intervenes to make life even hard
Evaluate the following integrals: (1)The integral of (6sin[2x])/sin(x)dx=____+C (2)The integral of (7-x)(3+[x^2])dx=____+C (3)The integral from 3 to 7 of ([t^6]-[t^2])/(t^4)dt=____+C (4)The integral of (6sin[x])/(1-sin^2[x])dx=____+C
Thank you in advance for your help. Evaluate the following integrals: (1)The integral from 1 to 7 of 5/t^4 dt (2) The integral from 0 to 1 of (6+[x]sqrt[x])dx (3)The integral from 7 to 8 of 2^t dt (4)The integral from 0 to 1/2 of 4/(sqrt(1-[x^2]))
Thank you in advance for your help. Evaluate the following definite and indefinite integrals: (1)The integral of (2x)/([x^2]+1)dx (2)The integral of [(arctan(x))/([x^2]+1)]dx (3)The integral of sqrt([x^3]+[1x^5])dx (4)The integral of (2+x)/([x^2]+1)dx (5)The integral of (2x)/([x^4]+1)dx (6)The integral from 0 to 2 of (x
Thank you in advance for your help. Evaluate the integrals by making the given substitution: (a)The integral of x(4+x^2)^3dx; (u=4+x^2) (b)The integral of ((sin sqrt[x])/sqrt[3x])dx; (u=sqrt[x]) (c)The integral of e^(3sin(t))cos(t)dt; (u=sin(t))
Thank you in advance for your help. Find the general indefinite integrals: (a)The integral of x(1+2x^2)dx (b)The integral of ((x^2)+1+(2/x^2+1))dx
If f is continuous for all real numbers, prove that the integral from a to b of f(x+c)dx=the integral from a+c to b+c of f(x)dx. For the case where f(x) is greater than or equal to 0, draw a diagram to interpret this equation geometrically as an equality of areas.
Water flows from the bottom of a storage tank at a rate of r(t)=200-4t liters per minute, where 0 is less than or equal to t and t is less than or equal to 50. Find the amount of water that flows from the tank during the first 10 minutes.
Consider the definite integral I 4 I = ∫ e^x dx 0 1. evaluate the integral I directly by use of a suitable anti-derivative. 2. evaluate the integral I by use of a suitable Riemann sum and formally limiting that sum 3. evaluate the integral I by use of the trapezoidal rule: a) I T,2 - for 2 sub
Derive an integration rule for the domain [0,1] based on the quadrature points x1=0, x2=1/3 and x3=1, which is exact for polynomials of degree <= 2. Please see attached for full question.
If C is the curve given by r(t) = (1 + 3 sin t) i + (1 + 5 sin^2 t) j + (1 + 5 sin^3 t) k, 0 ≤ t ≤ π/2 and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.
Calculate the following integrals: ∫ from 0 to ∞ x^¼/(x²+9) dx Please see attached for proper format.
Calculate the following integral... Please see attached for full question. Solution. Consider a close contour C shown above, where C consists of and a line segment from -R and R. Consider positive orientation, namely, clockwise. Choose r large enough so that are in the region covered by C. Let . By residual Theorem
Calculate the following integral: ∫ 0-->2pi e^(e^iθ) dθ Please see attached for full question.
Suppose f(x) is continuous and decreasing on the closed interval (4 is less than or equal to x is less than or equal to 11), that f(4)=6, f(11)=3, and that the integral as 4 goes to 11 of f(x)dx=27.01678. What is the integral as 3 goes to 6 of f^-1(x)dx?
"Evaluate the integral by interpreting it in terms of areas: the integral as 0 goes to 8 of |5x-10|dx"
Use the definition of integrals to evaluate the following integral: the integral as 1 goes to 8 of (2+3x-x^2)dx
Use the properties of integrals to verify the inequality without evaluating the integral: [the integral as 1 goes to 2 of (sqrt(5-x))dx] is greater than or equal to [the integral as 1 goes to 2 of (sqrt(x+1))dx].
This question has me going around in circles. I can't make the Sigma symbol on the computer, so I used the word "Sigma" instead. For (c), n is above the Sigma symbol and i=1 is below it. (a)Find an approximation to the integral as 0 goes to 4 of (x^2-3x)dx using a Riemann sum with right endpoints and n=8. (b)Draw a diagram
GAUSSIAN NUMERICAL INTEGRATION 1. Consider approximating integrals of the form... in which f(x) has several continuous derivatives on [0, 1] a. Find a formula... which is exact if f(x) is any linear polynomial. b. To find a formula... which is exact for all polynomial of degree ≤ 3, set up a system of four e
1. Show that if an integration formula of the form In ( f ) = ∑ wjf(xj) is exact when integrating 1, x, x2, ..., xm, then it is exact for all polynomials of degree ≤ m. Please see attached for proper format of question.
Let C be the curve which is the union of two line segments, the first going from (0, 0) to (3, -1) and the second going from (3, -1) to (6, 0). Compute the line integral. Please see attached.
∫x/[x + (x^1/2) -2]
Please assist me with the attached problems, including: Show that the improper integral converges and find its value or show that it diverges ... Please see attachment for complete list of questions.
Please assist me with the 30 attached problems, including: - Finding integral - Finding exact value - Finding volume - Finding length.
Please assist me with the attached problems. Examples: 2. Find each integral 5. Integrate equations using tables 6. Derive the sine squared formula 42. Use substituion to integrate certain powers of sine and cosine 52. Find the area of the region bounded by the graphs etc. (see attachment)
1. Find the volume of the solid generated by revolving the region enclosed by: {see attachment} 2. Find the arc length of the graph of the curve {see attachment} 3 - 7. Integrate attached equations ... 8. Find the limit of the improper integral: {see attachment} 9. Find the arc length of the curve given in parametric