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I find that hard to read. Do you mean ##\int \sin^n(x).dx = -\frac1n \sin^{n-1}(x)\cos(x) + \frac{n-1}n \int \sin^{n-2}(x).dx##? Looks right.Jbreezy said:There isn't it is (n-1)/n (times) the integral It isn't supposed to be in the denominator.
∫〖sin〗^n x dx= (-〖sin〗^(n-1) xcosx)/n)+ ((n-1)/n)∫〖sin〗^(n-2) x dx
thx
I don't understand how you got the first of those two equations. You should haveJbreezy said:##\int \sin^n(x).dx = -\frac1n \sin^{n-1}(x)\cos(x) + \frac{n-1}n \int \sin^{n-2}(x)cos^{2}.dx ##
They tell you to replace cosx^2 in the second integral and get to
##\int \sin^n(x).dx = -\frac1n \sin^{n-1}(x)\cos(x) + \frac{n-1}n \int \sin^{n-2}(x).dx##
I'm having trouble with that.
Integration by Parts is a technique used in calculus to find the integral of a product of two functions. It involves breaking down the integral into two parts and using a specific formula to solve for the integral.
Integration by Parts is used when the integral of a product of two functions cannot be easily solved using other techniques, such as substitution or the power rule. It is also useful when the integral involves trigonometric functions or logarithms.
The formula for Integration by Parts is ∫u dv = uv - ∫v du, where u and v are the two functions in the integral and du and dv are their respective differentials. This formula is also known as the "ILATE" rule, where I stands for inverse trigonometric, L for logarithmic, A for algebraic, T for trigonometric, and E for exponential functions.
When using the Integration by Parts formula, it is important to choose u and dv in a strategic way. A common method is to choose u as the function that becomes simpler when differentiated, and dv as the function that becomes easier to integrate when differentiated. This may require some trial and error and practice to become comfortable with.
Some common mistakes when using Integration by Parts include incorrect choice of u and dv, forgetting to apply the formula for the second integral, and making mistakes with integration. It is important to double check your work and practice regularly to avoid these mistakes.