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Bachelier
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How would you integrate this. I tried all integration methods available in Calculus II to no avail.
∫√(1+sin x) dx
∫√(1+sin x) dx
Bohrok said:Did you try u = sinx? That should give you something easy to work with.
lanedance said:is this indefinite or does it have limits? if there is limits you may be able to use the symmetry with cos to simplify things
The formula for integrating √(1+sin x) is ∫√(1+sin x) dx = 2√(cos x + 1) + C.
To solve integrals involving √(1+sin x), you can use the substitution method, where you substitute u = sin x and du = cos x dx. This will result in the integral becoming ∫√(1+u) du, which can be solved using the power rule.
No, the integral of √(1+sin x) cannot be evaluated using basic integration techniques. It requires the use of substitution and the power rule to solve.
The domain of integration for √(1+sin x) is all real numbers, as the function is defined for all values of x.
Yes, there are several real life applications of integrating √(1+sin x). One example is in physics, where this integral can be used to calculate the arc length of a curved path. It can also be used in engineering to determine the work done by a force over a curved path.