কুইজ রিভিউ: যোগজীকরণ - IUT - 30 Min

The area of the region bounded by x=0, y=8 and y=x2 is:

skipped

12 সঠিক উত্তর

Evaluated: int_(-3/4)^(3/4)( dx) / (√(9-4x^2)

correct

π/6 সঠিক উত্তর

π/4

π/3

π/2

Evaluate the integral int ex secx (1+tanx)dx -

incorrect

e-xcosx + c

exsec2x + c আপনার উত্তর

exsecx + c সঠিক উত্তর

exsinx + c

int_0^(π/2) cos^4xdx=?

correct

(3π)/16

সঠিক উত্তর

(2π)/3

(5π)/4

π/16

int x^2/(√(1-x^2) dx = ?

incorrect

1/2 x√1-x² + C আপনার উত্তর

1/2 cos-1x + 1/2 x √1-x² + C

(1/2x²)×√(1-x²) + C

1/2 sin-1x + 1/2 x√1-x² + C

blank সঠিক উত্তর

The area bounded by the curves y=2-x2 and y=x is :

correct

11/2

11/3

9/3

9/2

সঠিক উত্তর

Find the area of the region between the x-axis and the graph of f(x)=x3-x2-2x-1, -1≤x≤2.

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12/37

9/4

37/12 সঠিক উত্তর

4/9

int dx/(xsqrt(x^2-1))=?

correct

secx

sec-1x+C সঠিক উত্তর

sec-1x

secx+C

Evaluate int_3^7 xsqrt(x-3) dx

correct

111/3

189/4

144/5

সঠিক উত্তর

179/4

Suppose a pyramid has a square base of length 3 m in each side and a height of 5 m. What is the volume of that pyramid?

skipped

9 m³

15m³ সঠিক উত্তর

27m³

45m³

int tan^3 5x sec^2 5x dx =?

correct

1/12 sec^4 5x +C

1/20 tan^4 5x +C

সঠিক উত্তর

1/20 sec^4 5x +C

1/12 sec^3 5x +C

The area of the region enclosed by the curves y2 = x and y = x2 is -

incorrect

1/12 sq.unit

1/3 sq.unit

সঠিক উত্তর

1/2 sq.unit

1/6 sq.unit

আপনার উত্তর

Find the area of the region enclosed between the curves y = x2 and y = x + 6

correct

157/6

125/6

সঠিক উত্তর

95/6

13/6

int dx/(x+√x) = ?

correct

ln(√x+1)+c

tan-1(√x+1)+c

2ln(√x+1)+c সঠিক উত্তর

2tan-1(√x+1)+c

Find the integration of the following-

inte^x((1+sinx)/(1+cosx))dx

skipped

e2xcosx+c

2exsinx+c

extan(x/2)+c সঠিক উত্তর

e2xcot(x/2)+c

Find the area of the region enclosed by y=sqrt(2-x) and y = -x as shown in the figure given below ?

incorrect

22/3

10/3 সঠিক উত্তর

9/2

None of these আপনার উত্তর

int x^x (1+lnx) dx =?

correct

xx + c সঠিক উত্তর

x2x + c

x2xlnx + c

(1+lnx)/x +c

The maximum area of a rectangle (shown in the figure below) inscribed in a circle of radius 10 m is:

skipped

200m2 সঠিক উত্তর

225m2

169m2

288m2

int_0^lnsqrt2 (1+cos(e^(-2x)))/(e^(2x))dx =?

correct

1/8 +1/2 (sin 1 - sin(1/4))

1/4+1/2(sin1-sin(1/2))

সঠিক উত্তর

3/8+1/2(sin1-sin(1/4))

3/4+1/2(sin1-sin(1/2))

The region between the curve y=sqrt2 and the X-axis is revolved about the X-axis to generate a solid. Find its volume.

skipped

(8π)/3

(16π)/3

16π

8π

Blank সঠিক উত্তর

Evaluate intx/(1-x)^2dx

skipped

1/(1-x)+ln(1-x)+c সঠিক উত্তর

1/(1-x)-ln(1-x)+c

-1/(1-x)-ln(1-x)+c

-1/(1-x)+ln(1-x)+c

int_0^(π/2) cos ^3xsin^2xdx = ?

skipped

2/15 সঠিক উত্তর

2/13

π/4

π/2

int_0^2x/(sqrt(9-2x^2))dx

skipped

1 সঠিক উত্তর

int e^(-2x) tan(e^(-2x)) d=?

skipped

1/2 ln tan(e^(-2x))+C

1/2 lnsec(2^(-2x))+C

-1/2lncos(e^(-2x))+C

both b & c

blank সঠিক উত্তর

int_(1/2)^1 (dx)/(xsqrt(4x^2-1))=?

skipped

π/3 সঠিক উত্তর

π /6

3/2

2/3

Evaluate inte^x{1/(1-x)+1/(1-x)^2}dx

skipped

e^x/(1-x)+c সঠিক উত্তর

e^x/(x-1)+c

e^x/(1-x)^2+c

-e^x/(1-x)^2+c

The area of the region enclosed between the curves x = y^2-1 and x = |y|sqrt(1-y^2) is-

skipped

1 sq. units

3/4 sq. units

2/3 sq. units

2 sq. units সঠিক উত্তর

int_0^((3π)/4) |cosx | dx =?

skipped

sqrt2/2

1-sqrt2/2

2-1/sqrt2

সঠিক উত্তর

None of these

Partial fraction of (5x^2-4)/(x^2(x-2))is-

skipped

3/x+1/x^2+4/(x-2)

3/x^2+4/(x-2)

2/x+1/x^2+4/(x-2)

1/x+2/x^2+4/(x-2)

সঠিক উত্তর

In the following circle the area is Kπ what is the value of K?

skipped

18 সঠিক উত্তর

Evaluate : int_0^(π/2) cos^3 xsqrt(sinx) dx

skipped

5/21

-8/21

9/21

8/21

সঠিক উত্তর

Which one is correct for the partial fractions of5/((x-1)(3x+2))?

skipped

1/(x-1)-3/(3x+2)

সঠিক উত্তর

1/(x-1)+3/(3x+2)

3/(x-1)-5/(3x+2)

2/(x-1)-6/(3x+2)

What is the area of the shaded region of the following figure?

skipped

39 sq. unit

13 sq. unit

78 sq. unit সঠিক উত্তর

None of these

The figure given below shows triangle AOC inscribed in the region cut from the parabola y = x² by the line y=a² find the limit of the ratio if the area of the triangle to the area of the parabolic region as approaches zero.

skipped

3/4 সঠিক উত্তর

4/5

5/6

6/7

Find the area bounded by the curves y = x2 and y = 2x

skipped

4/3 সঠিক উত্তর

5/3

3/5

None of these

Find the area of the region enclosed by the graphs y = x - 1 and x = 3-y².

skipped

11/3

7/2

9/2 সঠিক উত্তর

13/3

The integral int(1+x-1/x)e^(x+1/x)dx is equal to:

skipped

(x-1)e^(x+1/x)+C

xe^(x+1/x)+C

সঠিক উত্তর

(x+1)e^(x+1/x)+C

-xe^(x+1/x)+C

∫ x2cosecx3dx= ?

skipped

1/3ln(cotx^3/2)+C

1/3ln(tanx^3/2)+C সঠিক উত্তর

ln(tanx^3/2)+C

ln(cotx^3/2)+C

যোগজীকরণ - IUT - 30 Min - 2026-03-30 02:52:06

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