area of the region bounded by y=e^x, y=1, x=-1

I did it by finding the integral from -1 to 0 of e^x -1 dx which becomes e^x - x from -1 to 0 which simplifies to 1/e +1 however the answer given says it is 1/e

Question

area of the region bounded by y=e^x, y=1, x=-1

I did it by finding the integral from -1 to 0 of e^x -1 dx which becomes e^x - x from -1 to 0 which simplifies to 1/e +1 however the answer given says it is 1/e

anonymous · Answer

for some reason i am getting 1 - 1/e are you sure the answer is right?

anonymous · Answer

The answer the book gives is 1/e

anonymous · Answer

OO sorry ok one min

anonymous · Answer

alright so do you know how to do double integrals?

anonymous · Answer

dividing the function into two separate integrals?

apoorvk · Answer

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Now we need to find the area of the shaded region in the plot, which is basically the area trapped under the y=e^x graph from '-1' to the point where the graph meets the the line y=1

now e^x=1 @ x= 0.


So we find definite integral of the function from '-1' to '0'

$$\int\limits_{-1}^{0}e^x.dx$$

evaluate this.