Math 116 exam 1 with correct answers 100% 2026

Math 116 exam 1 with correct answers 100% 2026 Width of an individual subdivision Δt. - Correct Answer Δt=(b-a)/n This is the width of an individual subdivision of a function f(t). ti - Correct Answer I = base+Δt right-hand sum - Correct Answer f(t1)Δt+f(t2)Δt+...+f(tn)Δt = (^n)(I=1)Σf(ti)Δt. left-hand sum - Correct Answer f(t0)Δt+f(t1)Δt+...+f(tn-1)Δt=(^n-1)(I=0)Σf(ti)Δt. definite integral - Correct Answer Suppose f is continuous for a=t=b. The definite integral of f from a to b, written as aSb f(t)dt. Is the limit of the left-hand or right-hand sums with n subdivisions of a=t=b as n gets arbitrarily larger, that is, as Δt-0. In other words, aSbf(t)dt=lim(n-inf)(left-hand sum) = limit as n goes to infinity of the sum of a left hand sum. aSbf(t)dt=lim(n-inf)(right-hand sum) = limit as n goes to infinity of the sum of a right hand sum. Each of these sums is called a Riemann sum, f is called the integrand, and a and b are called the limits of integration. How to compute definite integrals by hand. - Correct Answer Calculate the left and right-hand sum and then make n bigger so that you break up the function into more parts. The more parts the closer you are to the answer. The definite integral as an Area - Correct Answer When f(x)=0 and ab: Area under the graph of f and above x-axis between a and b =aSb(f(x)dx). Theorem 5.1: The Fundamental Theorem of Calculus. - Correct Answer If f is continuous on the interval [a,b] and f(t) = F'(t), then aSb(f(t)dt)=F(b)-F(a). Think of the antiderivative as f= velocity and F = position. To get velocity from position you do F', so F'(t)= f or the derivative of position is velocity or the antiderivative of velocity is position. Another view of the Fundamental Theorem of Calculus. - Correct Answer F(b)-F(a) = total change in F(t) between t=a and t=b