for #2 i think v= 7cos3a+8a^5...we can let m= (3a+8a^5) so dm/da = 3+40a^4
rewriting the equation will give v = 7cosm looks much more simple.... differentiating this = dv/dm = -7sinm since we want to find dv/da = dv/dm * dm/da this will give -7sin3a+8a^5 * 3+40a^4 simply substitute a= 1/2 TT into the equation to solve for dv/da when a = 1/2 TT
to integrate one must increase the power by 1 and divide the coefficient by the power.. for the question #3 the integral of 5sinb db. i think the d means integrate with respect to.. in this case its b the integral of sin will be -cos therefor this will give -5cos 1/2b^2 + c
for #5 im not sure but i think ∫5sinb + 9b^4 db = well the differential of sin is -cos so this will give -5cos 1/2b^2 + 9/5b^5 iam not sure of the 5 carries the minus sign or the cos..........
integration is just the opposite to differentiation. you increase the power by one then you divide the constant by the increased power. you normally end up with an equation of a line with an unknown y-intercept. if you have co-ordinates of a point on the line, you can make a substitution into the equation and solve for the y-intercept to get your final equation.
also like differentiation, you make the downstairs upstairs and if you have a combination of terms as we see in a quadratic equation for example, we integrate term by term to get the solution
Question 6. ∫5/x dx: If 1/x = ln x, would 5/x be 5lnx+ C? Since bringing the downstairs, upstairs..would ultimately result in x^-1+1=0 Then in this case y= c. Need some help understanding this.
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m = 8/e^t - e^t
ReplyDeleteAny down stairs bring upstairs
dm/dt = 8x^t - e^t
dm/dt = 8tx - e^t
v = 7 cos 3a + 8a^5. What is dv/da when a = 1/2 ∏
ReplyDeleteDifferntiating dv/da= -7 sin 3a + 40 a^4
I do not know how to do question 3
ReplyDeleteHelp with the integration
ReplyDeletedarky for #1 wouldnt m = 8e^-t - e^t when all downstairs are brought upstairs
ReplyDeleteand the differential will be -8t - e^t? help me if i am wrong
for #2 i think v= 7cos3a+8a^5...we can let m= (3a+8a^5)
ReplyDeleteso dm/da = 3+40a^4
rewriting the equation will give v = 7cosm
looks much more simple....
differentiating this =
dv/dm = -7sinm
since we want to find dv/da = dv/dm * dm/da
this will give -7sin3a+8a^5 * 3+40a^4
simply substitute a= 1/2 TT into the equation to solve for dv/da when a = 1/2 TT
to integrate one must increase the power by 1 and divide the coefficient by the power..
ReplyDeletefor the question #3
the integral of 5sinb db. i think the d means integrate with respect to.. in this case its b
the integral of sin will be -cos therefor this will give -5cos 1/2b^2 + c
the same goes for # 4 but this this time we integrate with respect to m.
ReplyDelete∫5cosm dm =
the integral of cos = ∫sin
therefore 5sin 1/2m^2 + c
for #5 im not sure but i think
ReplyDelete∫5sinb + 9b^4 db
= well the differential of sin is -cos so this will give -5cos 1/2b^2 + 9/5b^5
iam not sure of the 5 carries the minus sign or the cos..........
no i tink dat wrong..... its not -5 cos.. it jus 5 cosb.
ReplyDeletem = 8/e^t - e^t
ReplyDeletebring the down stairs upstairs
m= 8x^t - e^t
dm/dt= 8tx - e^t
This comment has been removed by the author.
ReplyDeleteintegration is just the opposite to differentiation. you increase the power by one then you divide the constant by the increased power. you normally end up with an equation of a line with an unknown y-intercept. if you have co-ordinates of a point on the line, you can make a substitution into the equation and solve for the y-intercept to get your final equation.
ReplyDeletealso like differentiation, you make the downstairs upstairs and if you have a combination of terms as we see in a quadratic equation for example, we integrate term by term to get the solution
ReplyDeletefor question 4
ReplyDeletethe∫5sinb db is -5cosb
the reason is dy/dx cosx = -sinx
but there is a policeman
for example the dy/dx -cosx = -*-sinx
a minus * minus = positive
so the integral of of -cosx = sinx
q6
ReplyDeletewe bring downstairs upstairs
then we integrate
we add one to the power
then we divide the coefficient by the new power
Question 6. ∫5/x dx:
ReplyDeleteIf 1/x = ln x, would 5/x be 5lnx+ C? Since bringing the downstairs, upstairs..would ultimately result in x^-1+1=0 Then in this case y= c. Need some help understanding this.
i did not notice thar
ReplyDeletebut dark angel you are right
the dy/dx lnx = 1/x
so ∫1/x = lnx
for #3:
ReplyDeletei think it goes like this:
integral of 5sinb= -5cos 1/2b^2
where integral of sin = -cos
for #6 i think you would work like:
ReplyDeleteintegral of 5/x = 5lnx + c
not sure though
Question 1
ReplyDeleteDifferentiate m = 8/e^t - e^t
first we simplify the equation
m = 8e^t - e^t
But in order to differentiate the equation we must make a substitution..
m = 8/e^t - e^t
ReplyDeletedm/dt = 8x^t - e^t
dm/dt = 8tx - e^t
Hey the best one:
ReplyDeletem = 8/e^t - e^t
when u bring downstairs upstairs isn't it suppose to be to a negative power.
also when y=e^t dy/dt= e^t
therefore your answer should be:
dm/dt = -8e^-t -e^t
differentiate m=8/e^t-e^t
ReplyDeletemultiply the equation
dm/dt=8x^t-e^t
dm/dt=8tx-e^t