- #1
Mathsishard123
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I have these integrals to find:
∫ (5x^2 + sqrt(x) - 4/x^2) dx
∫ [cos(x/2) - sin(3x/2)] dx
∫ s/sqrt(s^2 + 4) ds (upper coordinate is 5 lower coordinate is 1)
I have worked it out as:
∫〖(5x^2+√x〗-4/x^2) dx=5x^3/(2+1)+x^(1/2+1)/(1+1/2)-4x^(-2+1)/(-2+1)+C=5/3 x^3+2/3x^(3/2)+4/x+C
∫〖(cos(x/2)-sin(3x/2) )dx=2 sin(x/2)+2/3 cos(3x/2)+C〗
∫_1^5〖s/√(s^2+4)〗ds=1/2 √(s^2+4) (1≤s≤5)=1/2 (5^2+1)^(1/2)-1/2(1^2+1)^(1/2)=√26/2-√2/2
Do these look right?
∫ (5x^2 + sqrt(x) - 4/x^2) dx
∫ [cos(x/2) - sin(3x/2)] dx
∫ s/sqrt(s^2 + 4) ds (upper coordinate is 5 lower coordinate is 1)
I have worked it out as:
∫〖(5x^2+√x〗-4/x^2) dx=5x^3/(2+1)+x^(1/2+1)/(1+1/2)-4x^(-2+1)/(-2+1)+C=5/3 x^3+2/3x^(3/2)+4/x+C
∫〖(cos(x/2)-sin(3x/2) )dx=2 sin(x/2)+2/3 cos(3x/2)+C〗
∫_1^5〖s/√(s^2+4)〗ds=1/2 √(s^2+4) (1≤s≤5)=1/2 (5^2+1)^(1/2)-1/2(1^2+1)^(1/2)=√26/2-√2/2
Do these look right?