Question

Evaluating a Definite Integral as a Limit In Exercises 5-10, evaluate the definite integral by the limit definition. 6 3 5. \int_{2}^{6} 8 \,dx 6. \int_{-2}^{3} x \,dx 1 4 7. \int_{-1}^{1} x^{3} \,dx 8. \int_{1}^{4} 4x^{2} \,dx 2 1 9. \int_{1}^{2} (x^{2} + 1) \,dx 10. \int_{-2}^{1} (2x^{2} + 3) \,dx

          Evaluating a Definite Integral as a Limit In
Exercises 5-10, evaluate the definite integral by
the limit definition.
6
3
5. \int_{2}^{6} 8 \,dx
6. \int_{-2}^{3} x \,dx
1
4
7. \int_{-1}^{1} x^{3} \,dx
8. \int_{1}^{4} 4x^{2} \,dx
2
1
9. \int_{1}^{2} (x^{2} + 1) \,dx
10. \int_{-2}^{1} (2x^{2} + 3) \,dx

Evaluating a Definite Integral as a Limit In
Exercises 5-10, evaluate the definite integral by
the limit definition.
6
3
5. ∫2^6 8 dx
6. ∫-2^3 x dx
1
4
7. ∫-1^1 x^3 dx
8. ∫1^4 4x^2 dx
2
1
9. ∫1^2 (x^2 + 1) dx
10. ∫-2^1 (2x^2 + 3) dx

Added by Christopher Y.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sahil Patel

07/18/2019

Step 1

Step 1: The limit definition of a definite integral is given by: \[ \int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i^*) \Delta x \] where \(\Delta x = \frac{b-a}{n}\) and \(x_i^*\) is the sample point in the \(i\)th subinterval. Show more…

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Question 9. Evaluating a Definite Integral as a Limit In Exercises 5-10, evaluate the definite integral by the *limit definition*. Question 9 int_1^2 (x^(2)+1)dx Evaluating a Definite Integral as a Limit In Exercises 5-10, evaluate the definite integral by the limit definition. 5. 8 dx J2 6 x dx 7. x3 dx 8. 4x2 dx 9. (x2 + 1) dx 10. (2x2+ 3) dx 2