Question

4. Use one of the versions of the comparison theorem to estimate the following definite integrals (you are asked to come up with two numbers A, B such that $A le int_a^b f(x)dx le B$). (a) $int_{-1}^1 sqrt{1 + x^2} dx$; (b) $int_0^2 xe^{-x} dx$; (c) $int_0^1 e^{-x^2} dx$.

          4. Use one of the versions of the comparison theorem to estimate the following
definite integrals (you are asked to come up with two numbers A, B such
that $A le int_a^b f(x)dx le B$).

(a) $int_{-1}^1 sqrt{1 + x^2} dx$; (b) $int_0^2 xe^{-x} dx$; (c) $int_0^1 e^{-x^2} dx$.

4. Use one of the versions of the comparison theorem to estimate the following
definite integrals (you are asked to come up with two numbers A, B such
that A le inta^b f(x)dx le B).

(a) int-1^1 sqrt1 + x^2 dx; (b) int0^2 xe^-x dx; (c) int0^1 e^-x^2 dx.

Added by Caroline M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/21/2023

Step 1

Since x^2 is an increasing function on [1,3], we have: 1/(1+2) < J,Vi++z dx < 3/(3+2) Simplifying, we get: 1/3 < J,Vi++z dx < 3/5 So, we can estimate the value of the integral to be between 1/3 and 3/5. Show more…

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Use one of the versions of the comparison theorem to estimate the following definite integrals (you are asked to come up with two numbers A, B such that A ≤ ∫ₐᵅ f(x) dx ≤ B). (a) ∫₋₁¹ √(1 + x²) dx; (b) ∫₀² xe⁻ˣ dx; (c) ∫₀¹ e⁻ˣ² dx.