- #1
Giuseppe
- 42
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I was wondering what the best way to do this integral was:
Integral of 1+sin(x) all over cos(x)^2
Is subsitution the best way?
Integral of 1+sin(x) all over cos(x)^2
Is subsitution the best way?
The integral of 1+sin(x) all over cos(x)^2 represents the area under the curve of the function 1+sin(x) divided by the square of the function cos(x). This area can be interpreted as the total change in the function over a given interval.
To solve the integral of 1+sin(x) all over cos(x)^2, you can use the substitution method. Let u = cos(x) and du = -sin(x)dx. After substitution, the integral becomes -1/u^2 du, which can then be easily integrated to -1/u + C. Finally, substituting back in for u, we get -1/cos(x) + C as the final solution.
Yes, the integral of 1+sin(x) all over cos(x)^2 can also be evaluated using the trigonometric identity tan^2(x) = sec^2(x) - 1. By substituting this identity into the integral, we can then use the power rule to solve for the integral.
The domain of the function 1+sin(x) all over cos(x)^2 is all real numbers except for values of x where cos(x) = 0, as this would result in a division by 0 error. Therefore, the domain is (-infinity, -pi/2) U (-pi/2, pi/2) U (pi/2, infinity).
Yes, the integral of 1+sin(x) all over cos(x)^2 can be interpreted geometrically as the area under the curve of the function divided by the square of another function. This area can also be interpreted as the total change in the function over a given interval, as mentioned in the answer to the first question.