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Find the integral of a^(x) where a is a constant

Starting with ∫a x dx , We can re-write a x using logs as e ln(a)*x using some of their properties We use the substitution u = ln(a)*x (as such du/dx = ln(a)) allowing us to easily integrate e u with respect...
AP
Answered by Andreas P. • Maths tutor
3874 Views

Aidan, Emily and Seth shared some sweets in the ratio 2 : 7: 4 Seth got 16 more sweets than Aidan. Work out the total number of sweets they shared.

The difference in the ratio of Aidan's to Seth's sweets is 4-2=2 To find the scale factor to multiply up the ratio by, we divide the true difference in Aidan's and Seth's sweets by the difference in the rati...
EC
Answered by Eleni C. • Maths tutor
4949 Views

Solve the differential equation dx/dt=-6*x , given when t=0 x=7.

You start by seperating the variables giving, (1/x)*dx=(-6)*dt you then integrate both sides with respect to the variables, ln(x)=-6*t+c you then subsitute in the given conditions to find 'c', ln(7)=0+c ther...
LC
Answered by Lucy C. • Maths tutor
8891 Views

A ladder 6.8m long is leaning against a wall, the foot of the ladder is 1.5m from the wall, find the height that the ladder reaches up the wall.

Pythagorus' Theorem: A 2 + B 2 = C 2 Therefore... 1.5 2 + B 2 = 6.8 2 = 2.25 + B 2 = 46.24 B 2 = 46.24 - 2.25 = 43.99 SqR of 43.99 = 6.63m [The height the ladder reaches up the wall].
TG
Answered by Tom G. • Maths tutor
3899 Views

integrate x^2 + ln(x)

x^3/3 + 1/x
BM
Answered by Beth M. • Maths tutor
4138 Views