QUESTION
Which of the following definite integrals is equal to limn→∞∑k=1n12kncos(1+4kn)4nlimn→∞∑k=1n12kncos(1+4kn)4n ?
∫5112cosxⅆx∫1512cosxⅆx
the integral from, 1 to 5, of, 12 times cosine x, d x
A
∫513xcosxⅆx∫153xcosxⅆx
the integral from, 1 to 5, of, 3 x, times cosine x, d x
B
∫4012cos(1+x)ⅆx∫0412cos(1+x)ⅆx
the integral from, 0 to 4, of, 12 times the cosine of, open parenthesis, 1 plus x, close parenthesis, d x
C
∫403xcos(1+x)ⅆx
Question 2 Which of the following definite integrals is equal to $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{12 k}{n} \cos \left(1+\frac{4 k}{n}\right) \frac{4}{n} ?$ A $\int_{1}^{5} 12 \cos x \llbracket x$ (B) $\int_{1}^{5} 3 x \cos x d x$ (C) $\int_{0}^{4} 12 \cos (1+x) d x$ (D) $\int_{0}^{4} 3 x \cos (1+x) d x$
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