Calculus definite integral question?
The graph of y = cos x intersects the x-axis many times. If we consider the area between x = -π/2 and x - π/2, we can find the area between the curve and the x-axis by using ∫ cos x dx. The limits are from x = -π/2 to x = π/2.
Difficult definite integral question.?
Using the substitution x=2t-1, the definite integral ∫ (3 to 5) t sqrt(2t-1) dt may be expressed in the form k ∫ (a to b) (x+1)sqrt(x) dx, find the value of K+a+b
I need help with this Definite Integral question.?
yeah its right,only if lower limit is=a & upper =b. another way the ans. can be formed: you know lnx/y=lnx-lny therefore,ln4e-lne=ln4e/e =ln4 =2*ln2
Definite integrals question?
do you mean 0 upto 5 or as you wrote 5 upto 0?? ANSWER IS 1012/15 This is u-sub question with u = x+4 ===> du = dx and x = u-4 {limits will be changed to 4 to 9} Integral of (2x) sqrt(x+4) dx Integral of 2(u-4)sqrtu du ====> simplify integral of 2u^(3/2) - 8u^(1/2) du = 4/5 u ^5/2 - 16/3 u ^ 3/2 EVAL FROM 4 to 9 = 4/5(sqrt9)^5 - 16/3 (9^3/2) - [ 4/5(sqrt4)^5 - 16/3 (4^3/2) ] = 4/5*(3)^5 - 16*27 / 3 - 4/5*(2)^5 + 16/3*8 = 1012/15 =] ...
Definite Integrals. Looks like part of the questions is missing?
what happens when you interchange the limits ??? when the limits are the same ??? this is a " concept " question...and do you know them ??
Definite integrals??
Evaluate the following definite integral 1 / | 3 2 | x + 3 - 2 x - 2 x dx | / 0 next question: 7 / | 6 | x ln(x) dx | / 2
Definite Integral Question: ∫ (sin2x)dx from 0 to pi/2?
∫ (sin2x)dx from 0 to pi/2 ∫ (sin2x)dx from 0 to pi/2 u=2x du/2 = dx u(pi/2) = pi u(0) = 0 ∫ (sinu) (du/2) from 0 to pi -cosu / 2 -cos(2x) / 2 from 0 to pi (-1/2) - (-1/2) = 0 But my answer sheet saids = 1. What did I do wrong? cos(2x) / - 2 0, pi/2 [ cos2(pi/2) / - 2 ] - [ cos2(0) / - 2 ] [ cos(pi) / - 2 ] - [ cos(0) / - 2 ] [ - 1/2 ] - [ - 1/2 ] = 0 I'm not getting 1 either ways... 0, pi [ cosU / - 2 ] - [ cosU / - 2 ] [ cos(pi) / - 2 ] - [ cos(0) / - 2 ] [ - 1/2 ] - [ - 1/2 ] = 0
Evaluate the Definite Integrals: Calculus Questions (7 of em'--feel free to pick and choose)?
7 questions total--don't feel obligated to do all, unless u wanna!)Evaluate the definite integral... 1. sqrt.(9+3x)dx from 0 to 45 2. (x^18)(e^-x^19)dx from 0 to 1 3. dx/cubed root(64+4x)^2) from 0 to 61/4 4. dx/x*sqrt.(ln(x)) from e^9 to e^36 5. A bacteria population starts with 400 bacteria and grows at a rate of r(t) bacteria per hour. How many bacteria n will there be after three hours? (Give your answer to the nearest bacterium.) r(t)=450.263e^1.12567t n=______bacteria 6. Consider the continuous function f(x) which satisfies the condition below... f(x)dx=4 from 0 to 10, find the definite integral of f(2x)dx from 0 to 5 7. An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) liters per minute. How much oil V leaks out during the first hour? (Give your answer to the nearest liter.) r(t)-70e^-0.05t V=_______liters Thank you so much, I know it's a lot of questions here, don't feel pressured to answer all of them