Answer:
a. ∫ xSinx dx
iii. integration by parts
u =x and dv= sinx
b. ∫ x⁴/(1+x³). dx
ii. neither
Long division is an option here before integration is done
c. ∫ x⁴. e^x³. dx
i. substitution
where u = x⁵
d. ∫x⁴ cos(x⁵). dx
i. substitution
where u = x⁵
e. ∫1/√9x+1 .dx
i. substitution
where u = 9x+1
Hello,
Here is the demonstration in the book Person Guide to Mathematic by Khattar Dinesh.
Let's assume
P=cos(a)*cos(2a)*cos(3a)*....*cos(998a)*cos(999a)
Q=sin(a)*sin(2a)*sin(3a)*....*sin(998a)*sin(999a)
As sin x *cos x=sin (2x) /2
P*Q=1/2*sin(2a)*1/2sin(4a)*1/2*sin(6a)*....
*1/2* sin(2*998a)*1/2*sin(2*999a) (there are 999 factors)
= 1/(2^999) * sin(2a)*sin(4a)*...
*sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
as sin(x)=-sin(2pi-x) and 2pi=1999a
sin(1000a)=-sin(2pi-1000a)=-sin(1999a-1000a)=-sin(999a)
sin(1002a)=-sin(2pi-1002a)=-sin(1999a-1002a)=-sin(997a)
...
sin(1996a)=-sin(2pi-1996a)=-sin(1999a-1996a)=-sin(3a)
sin(1998a)=-sin(2pi-1998a)=-sin(1999a-1998a)=-sin(a)
So sin(2a)*sin(4a)*...
*sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
= sin(a)*sin(2a)*sin(3a)*....*sin(998)*sin(999) since there are 500 sign "-".
Thus
P*Q=1/2^999*Q or Q!=0 then
P=1/(2^999)
Answer:
(a) (-12/13, 5/13)
(b) (12/13, -5/13)
(c) (-12/13, -5/13)
(d) (12/13, 5/13)
Step-by-step explanation:
(a) The terminal point is effectively reflected across the y-axis, so the sign of the x-coordinate changes. (-12/13, 5/13)
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(b) The terminal point is effectively reflected across the x-axis, so the sign of the y-coordinate changes. (12/13, -5/13)
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(c) The terminal point is effectively reflected across the origin, so the signs of both coordinates change. (-12/13, -5/13)
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(d) The terminal point is mapped to itself, so its coordinates remain unchanged. (12/13, 5/13)
(13-0.25x4)(12+4x4)=2,464
(13-0.25x5)(12+4x5)=3,845
(13-0.25x6)(12+4x6)=2,845
so your answer is 3,845 because if Hirome sells them for $11.75 he makes $3845 if Hirome sold them for $11.50 he makes $2845.80 and if he sold them for $12.00 he would make $2464.00
