Problem 5 Consider the area between the graphs x+2y=4 and x+4=y^2. This area can be computed in two different waysusing integrals. First of all it can be computed as a sum of two integrals. ∫[upper limit =b, lower limit=a]f(x)dx + ∫[upper lim=c, lower=d]g(x)dx where a=_______ , b=________, c=_______ and f(x)=________ and g(x)=_________ Alternatively this area can be computed as a single integral ∫[upper limit=beta, lower limit=alpha]h(y)dy where alpha=______, beta=_______ , and h(y)=________ Either way we find that the area is________
Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Problem 5
Consider the area between the graphs x+2y=4 and x+4=y^2. This area can be computed in two different waysusing integrals. First of all it can be computed as a sum of two integrals.
∫[upper limit =b, lower limit=a]f(x)dx + ∫[upper lim=c, lower=d]g(x)dx
where a=_______ , b=________, c=_______ and f(x)=________ and g(x)=_________
Alternatively this area can be computed as a single
∫[upper limit=beta, lower limit=alpha]h(y)dy
where alpha=______, beta=_______ , and h(y)=________
Either way we find that the area is________
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