Final answer:
The integral of sinh(x) from 0 to 2 is the difference between cosh(2) and cosh(0), which involves evaluating the antiderivative, cosh(x), at the limits of integration.
Step-by-step explanation:
The value of the integral of sinh(x) from 0 to 2 can be found using the definition of the hyperbolic sine function and the fundamental theorem of calculus. The hyperbolic sine function, sinh(x), is defined as (ex - e-x)/2. When integrating sinh(x), we use its antiderivative, which is cosh(x), another hyperbolic function representing the cosine hyperbolic. The integral is then calculated by evaluating the antiderivative at the upper and lower limits of integration and finding the difference:
- First, find the antiderivative of sinh(x), which is cosh(x).
- Next, evaluate cosh(x) at x = 2 and x = 0.
- Lastly, subtract the value of cosh(0) from cosh(2) to find the value of the integral from 0 to 2.
The integral of sinh(x) from 0 to 2 is equal to cosh(2) - cosh(0).