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Aliun [14]
3 years ago
7

Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim

||Δ|| → 0 n (4ci + 11) i = 1 Δxi [−8, 6]
Mathematics
1 answer:
geniusboy [140]3 years ago
5 0

Answer:

The corresponding definite integral may be written as

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x

The answer of the above definite integral is

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98

Step-by-step explanation:

The given limit interval is

\lim_{||\Delta|| \to 0}  \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i

[a, b] =  [-8, 6]

The corresponding definite integral may be written as

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x

\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x

Bonus:

The definite integral may be solved as

\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98

Therefore, the answer to the integral is

\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x  = 98

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