9000150407
Level:
A
Evaluate the following definite integral.
\[
\int _{1}^{2}7^{x}\, \text{d}x
\]
\(\frac{42}
{\ln 7} \)
\(49\ln 7\)
\(42\)
\(42\ln 7\)
Definite Integral
9000150408
Level:
A
Evaluate the following definite integral.
\[
\int _{0}^{ \frac{\pi }{
4} } \frac{2}
{\cos ^{2}x}\, \text{d}x
\]
\(2\)
\(0\)
\(4\)
\(\pi \)
9000150405
Level:
B
Evaluate the following definite integral.
\[
\int _{-1}^{3} \frac{1}
{2x + 3}\, \text{d}x
\]
\(\ln 3\)
\(\ln 1\)
\(\ln 9\)
\(2\ln 9\)
9000150406
Level:
B
Evaluate the following definite integral.
\[
\int _{-3}^{2} \frac{x}
{x^{2} + 3}\, \text{d}x
\]
\(\frac{1}
{2}\ln \frac{7}
{12}\)
\(2\ln \frac{12}
{7} \)
\(2\ln \frac{7}
{12}\)
\(\frac{1}
{2}\ln \frac{12}
{7} \)
9000150401
Level:
A
Evaluate the following definite integral.
\[
\int _{-3}^{1}(x^{2} + 3x)\, \text{d}x
\]
\(-\frac{8}
{3}\)
\(\frac{8}
{3}\)
\(-\frac{64}
{3} \)
\(\frac{64}
{3} \)
9000150402
Level:
A
Evaluate the following definite integral.
\[
\int _{-\frac{\pi }{
2} }^{ \frac{\pi }
{2} }\sin x\, \text{d}x
\]
\(0\)
\(\pi \)
\(2\)
\(1\)