Question

Approximating the integral \int_0^{10} 2^x dx with i) the Trapezoidal Rule with $n = 4$, yields $\int_0^{10} 2^x dx \approx$ The error in this approximation is ii) Simpson's Rule with $n = 2$, yields $\int_0^{10} 2^x dx \approx$

          Approximating the integral
\int_0^{10} 2^x dx
with
i) the Trapezoidal Rule with $n = 4$, yields
$\int_0^{10} 2^x dx \approx$
The error in this approximation is
ii) Simpson's Rule with $n = 2$, yields
$\int_0^{10} 2^x dx \approx$

Approximating the integral
∫0^10 2^x dx
with
i) the Trapezoidal Rule with n = 4, yields
∫0^10 2^x dx ≈
The error in this approximation is
ii) Simpson's Rule with n = 2, yields
∫0^10 2^x dx ≈

Added by Steven T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Diogo Caetano

Step 1

The Trapezoidal Rule approximates the integral by dividing the interval [a, b] into n equal subintervals and approximating each subinterval with a trapezoid. The formula for the Trapezoidal Rule is: ∫(a to b) f(x) dx ≈ (b - a) * [(f(a) + f(b))/2] In this case, Show more…

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ii) The last question is: What is the error in this approximation? Approximating the integral âˆ«10 2dx with the Trapezoidal Rule with n=4 yields 12dx. The error in this approximation is: ii) Simpson's Rule with n=2 yields âˆ«10 2dx.