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Solve: `int sqrt(4x^2 + 5)dx`
Concept: Methods of Integration> Integration by Parts
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Concept: Methods of Integration> Integration by Substitution
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Concept: Methods of Integration> Integration by Substitution
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Concept: Methods of Integration> Integration by Parts
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
Concept: Area Under Simple Curves
Find the area of the region bounded by the following curves, the X-axis and the given lines:
y = x2 + 1, x = 0, x = 3
Concept: Area Under Simple Curves
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
Concept: Area Under Simple Curves
Using definite integration, area of the circle x2 + y2 = 49 is _______.
Concept: Area Under Simple Curves
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Concept: Area Under Simple Curves
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5.
Concept: Standard Forms of Parabola and Their Shapes
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
Concept: Area Under Simple Curves
The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`
Concept: Area Under Simple Curves
Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3
Concept: Area Under Simple Curves
Find the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3
Concept: Area Under Simple Curves
Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5
Concept: Area Under Simple Curves
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
Concept: Area Under Simple Curves
The area of the region bounded by the curve y = x2, x = 0, x = 3, and the X-axis is ______.
Concept: Area Under Simple Curves
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
Concept: Area Under Simple Curves
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
Concept: Area Under Simple Curves
Determine the order and degree of the following differential equation:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Concept: Order and Degree of a Differential Equation
