00:01
Hello everyone, so we have a function y is equal to f of x.
00:05
So this is a particular solution of d y divided by d x is equal to e to the power x minus 1 divided by e to the power x.
00:15
With the condition, f of 1 is equal to 0.
00:19
We need to find the value of f of minus 2.
00:22
And the options that we have are option a, which is 0 .217, option b, which is 0 .349, option c, which is 0 .540, and option b, which is 0 .759.
00:42
So let's jump on to the solution of the question.
00:45
So we've been given, d .y divided by dx is equal to e to the power x minus 1 divided by e to the power x.
00:52
Transpose this cross multiply.
00:55
So e to the power y.
00:58
This is e to the power y.
01:03
E to the power y, dy, is equal to e to the power x minus 1 dx.
01:12
So on integrating this, on integrating, this is going to be integration of e to the power y, dy is equal to e to the power x minus 1, dx integration.
01:31
So this is going to be equal to e to the power y is equal to e to the power x minus x plus an arbitrary so when x is equal to 1, y would be equal to 0, e to the power 0 is equal to e to the power 1 minus c...