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Integrate 10 divided by x square?
-(10/x)
How do you integrate functions?
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
What do integrate mean?
In calculus, "to integrate" means to find the indefinite integrals of a particular function with respect to a certain variable using an operation called "integration". Synonyms for indefinite integrals are "primitives" and "antiderivatives". To integrate a function is the opposite of differentiating a function.
What is the integral of 2-2x with limits 0 to t?
Integrate(0->t) (2-2x) dx is the integral correct (Integrate(0->t) (2-2x) dy would be different, you must state integrate with respect to what otherwise it can be anything) So integrals preserves sum and product with constants. i.e. Integrate (2-2x) dx = Integrate 2 dx - 2integrate x dx = 2x - x^2 + C By Fundamental Theorem of Calculus, take any anti-derivative, say C = 0 would be fine, and Integral(0->t)(2-2x) dx = (2x-x^2)|(0->t) = (2t-t^2) - 0 = 2t-t^2 It is a special case of the Second Fundamental Theorem of Calculus -- integral(0->t) f(x) dx is an anti-derivative of f(x).
How can you integrate a three variable functions?
Assuming you are integrating with respect to one of the three variables, you integrate normally. For example: ∫(x+y+z)dx = ∫ x dx + ∫ y dx + ∫ z dx (Integral of the sum is the sum of the integrals) = x^2/x + yx + zx + C Or a harder one: ∫ (sin^2(y)+sqrt(z))/x dx = (sin^2(y) + sqrt(z))*∫ 1/x dx (Factor out constants) = ln(x)*(sin^2(y) + sqrt(z)) tl;dr: just do it normally with normal integration rules
