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use product-to-sum
formula sin u cos v =
1/2 [sin(u+v)
+ sin(u-v)]
so you get
1/2 int: (sin 15x) - (sin5x) dx
split it
1/2 int: sin 15x dx
- 1/2 int: sin 5x dx
using substitution you can conclude that
1/30 int: sin u du
- 1/10 in sin w dw
(you get the fraction change when you set dx=
du
and dw)
so then
- (cos u)/30 + (cos w)/10
replace the substitution
(cos 5x)/10 - (cos 15x)/30 + Constant
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What is the integral of 10x?
∫ 10x dx Factor out the constant: 10 ∫ x dx Therefore, by the power rule, we obtain: 10x(1 + 1)/(1 + 1) + k = 10x²/2 + k = 5x² + k
5x-15x plus 10?
5x-15x+10 = 10-10x when simplified Assuming a request to solve the equation: 5x -15x + 10 = 0 5x - 15x + 10 = 0 5x - 15x = -10 or (multiplying everything by -1 gives you -5x + 15x = 10) so 15x - 5x = 10 10x = 10 x =1
Integral of xlnxdx?
integration by parts. Let u=lnx, dv=xdx-->du=(1/x)dx, v=.5x^2. Integral of (xlnxdx)=lnx*.5x^2-integral of .5x^2(1/x)dx=lnx*.5x^2-integral of .5xdx=lnx*.5x^2-(1/6)x^3. That's it.
The measures of the exterior angels of a convex quadrilateral are 90 degrees 10x degrees 5x degrees and 45 degrees What is the measure of the largest exterior angel?
150 degrees
What is the limit as x approaches zero of 5x divided by 3sinxcosx?
1.6667
Integration of cos 5x?
The integral of cos 5x is 1/5 sin (5x)
Int sin 3x cos 5x dx?
integral sin(3 x) cos(5 x) dx = 1/16 (8 cos^2(x)-cos(8 x))+C
Int cos 10x cos 15x dx?
There is some kind of formula here, half angle, or some such that I forget, but I do remember the algorithm. So...,int[cos(10X)cos(15X)] dxsince this is multiplicative, switch it aroundint[cos(15X)cos(10X)] dxint[cos(15X - 10X)/2(15 -10) + cos(15X + 10X)/2(15 + 10)] dxint[cos(5X)/10 + cos(25X)/50] dx= 1/10sin(5X) + 1/50sin(25X) + C=========================
What is 10x minus 5x plus 5x?
10x - 5x + 5x = 10x
-10x plus 5x?
-10x + 5x = -5x
What is the integral of 10x?
∫ 10x dx Factor out the constant: 10 ∫ x dx Therefore, by the power rule, we obtain: 10x(1 + 1)/(1 + 1) + k = 10x²/2 + k = 5x² + k
Integral of (sin2x)(cos3x)?
Int[sin(2x)*cos(3x)]dx = Int[(2sinx*cosx)*(4cos^3x - 3cosx)]dx= Int[(8sinx*cos^4x - 6sinx*cos^2x)]dx Let cosx = u then du/dx = -sinx So, the integral is Int[-8*u^4 + 6*u^2]du = -8/5*u^5 + 2u^3 + c where c is a constant of integration = -8/5*cos^5x + 2cos^3x + c
What is 10x times 5x?
10x * 5x = 50x2 =====
10x divided by 5x?
10x ÷ 5x = 2
How do you factor out 5x plus 10x?
5x + 10x doesn't need factorization as you can just add them up (5x+10x=15x). However, if you really want to, 5x+10x=5x(1+2)=5x(3)=15x
What is the answer to 10x plus 7 equals 5x plus 32?
10x+7 = 5x+32 10x-5x = 32-7 5x = 25 x = 5
5x plus 4 equals 10x-5 equals?
5x + 4 = 10x - 5 10x - 5x = 4 + 5 5x = 9 x = 1.8
