- #1
lovemake1
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Homework Statement
Integral of ...
h(x) = x^5 + x^5 + [cos(x)]^6
Homework Equations
The Attempt at a Solution
so it would be
1/6x^6 + 1/6x^6 + 1/7[sin(x)]^7
is this correct?
Probably not, but you won't see the first form you wrote very often.lovemake1 said:wait is there diference between
cos(x)^6 and [cos(x)]^6
lovemake1 said:Integral of ...
h(x) = x^5 + x^5 + [cos(x)]^6
To solve this integral, you can use the trigonometric identity cos2(x) = (1 + cos(2x))/2 to rewrite [cos(x)]6 as (1 + cos(2x))3/8. Then, you can use the power rule for integration and the substitution method to solve the integral.
No, this integral cannot be solved using a calculator. You will need to use integration techniques and trigonometric identities to solve it by hand.
The degree of this integral is 5, as it contains only terms with the variable x raised to the fifth power.
Yes, you can use the Pythagorean identity sin2(x) + cos2(x) = 1 to rewrite the integral as x5 + x5 + (1 - sin2(x))3/8. Then, you can use the power rule for integration and the substitution method to solve the integral.
Yes, if the limits of integration are from 0 to π/2, the integral can be simplified to π/8 + 3/8. This is because cos(0) = 1 and cos(π/2) = 0, making the first and second terms in the integral equal to 0.