quick calculus verification?

Question

hi this is my question
find the integral of the following equation
f(x)=(1/10)e^x(t-1/10) 0
i get this to equal to (1/10)e^0(t-1/10) is this correct or did i do something wrong? thanks

perhaps this might clear it up
f(x)=(1/10)e^[x*(t-1/10)] i get that the 1/10 can become a constant so the anti derivitive of e^[x*(t-1/10)] should equal e^[0*(t-1/10)] rite?(given the interval [0,infinity)

Answer 1

OK.
The indefinite integral of e^(bx) is (1/b) * e^(bx).
The indefinite integral of ae^(bx) is (a/b) * e^(bx).

In a definite integral, if you evaluate e^(bx) at infinity, you get divergence if b is positive or zero, and 0 if b is negative.

If you evaluate e^(bx) at 0, you get e^0, which is more commonly known as 1.

So the definite integral of ae^(bx) from 0 to infinity either diverges or equals -a, depending on the sign of b.

In this case, a = 1/10 and b = t-1/10.

Answer 2

If x is your variable of integration, the (t-1/10) can come
outside the integral. But then the integral clearly diverges.
Did you write this correctly?