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What is the integral of 2?
The integral of 2 is "who gives a $%&#." You need to know what 2 is relating to and what the 2 means. If the question is "What is the integral of 2 dx" the answer would be "2x + c," with c being a constant. If you instead wish to know what the integral of 2 dy, the answer is very different. (2y +c)
How do you express an iterated integral in six different ways?
First, draw the region/solid being bounded by parameters say: y^2 + z^2 = 9, x = -2, and x = 2 Now analyze what possible iterated integrals can be used to find this region. the two "main" iterated integrals are: the triple integral from [-2,2] [-3,3] [-sqrt(9-y^2),sqrt(9-y^2)] dz dy dx and [-2,2] [-3,3] [-sqrt(9-z^2),sqrt(9-z^2)] dy dz dx Now, instead of sketching every region to find the different possible integrals, using the rules of triple integration, they will essentially be any legal alteration of the order of the "main" integrals. essentially, the first main integral can be rewritten as dx dz dy, and dz dx dy the second can be written as dx dy dz and dy dx dz.
What is the integral of 3 x square?
Int = 3x^(2) dy y = 3x^(3) / 3 + c y = x^(3) + C
What is the integral of a function of x when x is itself a function of y with respect to x?
If x = g(y) ∫ f(x) dx = ∫ f(g(y))g'(y) dy This is called change of variables.
How do you Differentiate and Integrate y equals 3 to the power of x?
dy/dx = 3^x * ln(3)integral = (3^x) / ln(3)To obtain the above integral...Let y = 3^xln y = x ln 3y = e^(x ln 3)(i.e. 3^x is the same as e^(x ln 3) ).The integral will then be 3^x / ln 3 (from linear composite rule and substitution after integration).
