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What is the indefinite integral ∫5exp(3-4x)dx ?

∫ 5e 3-4x dx=5∫e 3 e -4x dx=5e 3 ∫e -4x d=5e 3 [(-1/4)e -4x ]=-(5/4)e 3 e -4x =-(5/4)e 3-4x
AM
Answered by Alexandros M. • Maths tutor
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The mass, m grams, of a substance is increasing exponentially so that the mass at time t hours is m=250e^(0.021t). Find the time taken for the mass to double in value.

All exponential equations can be reduced to the form m=m 0 e kt , where m 0 is the initial mass. This means for our equation the initial mass is 250g. If the mass has doubled in size, then m now equals 2*250...
TJ
Answered by Tom J. • Maths tutor
8974 Views

How can I determine the stationary points of a curve and their nature?

For example, y = 3x 3 + 9x 2 + 2. Determine the stationary points and their nature. Let's remind ourselves what a stationary point is, and what is meant by the nature of the points. A stationary point is a p...
TD
Answered by Tutor87017 D. • Maths tutor
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Find all the solutions of 2 cos 2x = 1 – 2 sinx in the interval 0 ≤ x ≤ 360°.

We know that having cos and sin functions in a question is going to cause us problems - we need a single function of x. So, step 1, we need to rewrite sin or cos in terms of the other. How do we choose which...
NH
Answered by Nicola H. • Maths tutor
24156 Views

Find the indefinite integral of sin(2x)(cos^2(x)) with respect to x.

We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)). Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x). We can now split the integral into...
PP
Answered by Patrick P. • Maths tutor
6299 Views