Indefinite Integrals and the Net Change Theorem

Evaluate the definite integral.

• 3
• 9/2
• 9
• Not possible

_{Evaluate the integral}

• 30/3
• 31/3
• 29/3
• 32/3

• 12/3
• 6.5
• 5.5
• 11/3

What should be assigned to u in the integral below?

∫(xsin(2x²))dx

• 2x²

• 4x

• 5x

• no u substitution needed

What should be used for u in solving the integral below
∫ (tan⁴xsec²x)dx

• tanx
• tan⁴x
• no u needed
• tanxsecx

Solve the following integral. Leave your solution in term of u.

∫ √(4x-3) dx

• (1/6)(√u)³ + c

• (2/3)u^3/2 + c

• (1/4)u^1/2 + c

• (1/4)u^3/2 + c

∫ sin (2x) dx

• cos(2x)+C

• -(1/2)cos(2x)+C

• -cos(2x)+C

• (1/2)cos(2x)+C

• -½x^-2 + C
• -⅖x^-5/2 + C
• 2x^1/2 + C
• -2x^-1/2 + C

Find the area under a curve defined by the equation 5x⁴+3x+7 between the x values 0 and 4.

• 1200
• 1/12
• 1134
• 1076

What does C represent in an antiderivative?

• A variable
• A constant
• None of these
• Unknown